2.Two angles that form a linear pair are always supplementary. (b) making a linear pair No, but they're "supplementary".Two "complementary" angles add up to 90°. ∴ AB || CD 1 decade ago. (a) 95°, 85° Find the sum 2a +b. (b) Let the angle be x. A transversal intersects two or more than two lines at _________ points. Then, which of the following is true? ⇒ 2x + x = 180° ⇒ b = c – a Since, l || m and q is a transversal The legs of a stool make an angle of 35″ with the floor as shown in figure. 8. In the given figure, l || m || n. ∠OPS = 35° and ∠QRT = 55°. Solution: \(\Rightarrow \quad x=\frac{180^{\circ}}{4}=45^{\circ}\) ∴ ∠AOE + ∠EOD + ∠DOB = 180° ∴ ∠2 + 135° = 180° [Co-interior angles] If the complement of an angle is 799, then the angle will be of (d) Since, PQ || RS, line l is a transversal. Question 67. If ∠POR = 90° and x : y = 3 : 2, then z is equal to ⇒ ∠QPR = 130° – 50° = 80°, Question 11. True Question 96. Thus, a = 67° and b = 48°, Question 102. (b) 46° (d) We have, Give reason in support of your answer. The angles between North and West and South and East are l || m and QR is a transversal. \(\Rightarrow \quad x=\frac{88^{\circ}}{4}=22^{\circ}\) Supplementary and complementary refer to only a pair(two) of angles. Question 2. Solution: Question 66. (d) Since PQ I RS and line 1 is a transversal. They just need to add up to 90 degrees. (ii) ∠POS and ∠SOQ; ∠POR and ∠ROQ are two pairs of supplementary angles. (a) vertically opposite angles ∠AOF=∠COD [Vertically opposite angles] 60° + y = 90° (b) corresponding angles Solution: (iii) No, a and b are not adjacent angles as they don’t have common vertex. Two angles are equal and su... maths. Answered By . (c) a is false and b is true but ∠2 + ∠3 = 180°, Question 39. Question 1. Two angles are “equal and supplementary” to each other. (iii) If both angles are right angle (equal to 90), then their sum is always equal to 180. Question 9. Hence, ∠a = 30°, ∠b = 150°, ∠c = 150°. ∴ a = 20° [Alternate interior angles] Solution: In other words, if two angles add up to form a right angle, then these angles are referred to as complementary angles. Since, a transversal intersects two parallel lines, then interior angles on the same side of a transversal are supplementary. (c) ∠3 + ∠8 = 180° If ∠x = ∠y = ∠z, then ∠x and ∠y; ∠y and ∠z; ∠z and ∠x are three pairs of complementary angles. Question 19. Angles /_A and /_B are supplementary if their sum measures 180^o. Solution: (a) ∠1 + ∠5 = 180° . Question 21. Find the angles x and y. As if both adjacent angles are acute angles, then they do not form a linear pair. Question 103. (a) 126° A + B = 90° (d) 45°, 35° Opposite, Question 49. Solution: \(\Rightarrow x=\frac{180^{\circ}}{3}=60^{\circ}\) ∴ ∠1 = 34° [Alternate interior angles] Now, AB || DC and BC is a transversal. Solution: (ii) one arm is always common, and ⇒ B = 90° – A always. Thus, x = 114° and y = 132°, Question 108. ⇒ 3a – b + 2a + b = 180 ⇒ 5a = 180 (d) ∠AOC and ∠BOC form a pair of supplementary angles. ∠a = ∠3 [Vertically opposite angles] In the given figure, if AB || CD, ∠APQ = 50° and ∠PRD = 130, then ∠QPR is ∴ Supplement of x = 180° – 28° = 152°, Question 88. (ii) Name all the pairs of complementary angles. (a) both p and q are true This site is using cookies under cookie policy. ∴ ∠RSC + ∠CSF = 180° [Linear pair] (iii) Let the angle between d and fis ∠3. ⇒ 5b – 180° – 80° = 100° (b) 125° (c) m and n are two straight lines and I is a transversal intersecting both lines m and n. (d) 119° Question 104. As ∠UVQ and ∠ROF are corresponding angles and are not equal. Now, a + b = 45° + 55° = 100°, Question 105. (b) Since, PA || BC and AB is a transversal. Solution: The angle The angles x and 90° – x are Now, ∠PQR = ∠PQU + ∠UQR ⇒ 5a = 180° – 130° = 50° Solution: Again, ∠PQR and ∠QRP are complementary as ∠PQR + ∠QRP = 40° + 50° = 90°. Solution: (a) Seven football players are practicing their kicks. a complementry angle … ∴ y = 2 × 18° = 36° ∠1 +∠2 = 180° [Angles on a straight line PQ] The proposition continues by stating that on a transversal of two parallel lines, corresponding angles are congruent and the interior angles on the … Find ∠EFD. ⇒ x = 360° – 2x – 60° We have, Now, l is also parallel to CD and FG is a transversal. True, Question 63. Find ∠QUR. (a) If one of the angles is acute, then other angle of a linear pair is obtuse. Now, c || d and e is a transversal. Solution: Now, e || f and c is a transversal. (a) ∠1 = ∠5 S. Two vertical angles are congruent. In the given figure, line I intersects two parallel lines PQ and RS. ⇒ (3a + 5)° + (2a-25)° = 180° Solution: ∴ ∠RST + a = 180° [Linear pair] Solution: Also, BC || DT and DC is a transversal. ⇒ f = 108°, Question 37. They are lined up in a straight line in front of the goalpost [See fig.(i)). You can specify conditions of storing and accessing cookies in your browser. (b) 50° (c) 55° ∴ ∠2 + 3 = 180° [Co-interior angles] Question 87. Thus, one angle is 45° and other is 180° – 45° = 135°, Question 98. Question 45. Given that ∠AOB = 90° [∵ OB ⊥ OA] false . For example: This is always true! (c) 72° Also, AB || DF and BD is a transversal. Two adjacent angles always form a linear pair. (b) Given that a : b = 3 : 2 3.Two angles that are congruent are sometimes right. \(\Rightarrow \angle A B P=\frac{134^{\circ}}{2}=67^{\circ}\). True, Question 69. (a) 20°, 50° (b) In a pair of adjacent angles, vertex is always common, one arm is always common and their non-common arms are on either side of the common arm. Supplementary, Question 44. If the sum of measures of two angles is 180° then they are _________ Find the angles. sometimes. Question 61. Solution: Now, AB || CD and ED is a transversal. (c) ∠a + ∠d = 180° Vertically opposite angles are either both acute angles or both obtuse angles. From (i), (b) 75° 7 Answers. Solution: (b) Since, PQ || ST and SO is a transversal. (c) Since, PQ || RS and line 1 is a transversal. alternate interior angles have one common _________ (a) 90° ∴ ∠QOR = 3y = 3× 30° = 90°, Question 15. The sum of two opposite angles of a parallelogram is 150 degree .find the measure of each of its angles. ⇒ ∠POR + ∠QOS = 180° – 90° = 90° ——- (i) Solution: Also, ∠EFG = ∠1 + ∠2 – 34° +45° = 79° We hope the NCERT Exemplar Class 7 Maths Chapter 5 Lines and Angles will help you. ⇒ ∠COA – 41° ——— (i) \(\Rightarrow x=\frac{120^{\circ}}{2}=60^{\circ}\) (b) 15° As ∠EPQ and ∠GQP are interior angles on the same side of transversal AB and are supplementary Now, QP || RS and PR is a transversal. always. The difference of two complementary angles is 30°. ⇒ x + 210° = 360° Let x = 3k and y – 2k Solution: The angles x – 10° and 190° – x are (d) ∠3 = ∠7 (a) 5b + 2a = 180° [Linear pair] (c) 100°, 60° (a) 44° Also, p || q and l is a transversal. Question 82. \(\Rightarrow \quad b=\frac{120^{\circ}}{3}=40^{\circ}\) Sign in:P. 1 decade ago. Yes. Solution: (i) b and c Acute, Question 54. Solution: What is the type of other angle of a linear pair if If the two complementary angles are adjacent then they will form a right angle. 90°, Question 55. ∴ ∠3=68° ——– (i) [Corresponding angles] Hence, in this case these two angles are considered congruent. Solution: Both the supplementary angles are 90 degrees each. Upvote(0) How satisfied are you with the answer? In the given figure, if PQ || RS and QR || TS, then the value of a is (d) 120° ⇒ ∠Q = 180° – 60° = 120°, Question 13. (a) interior angles on the same side of the transversal In the given figure, lines PQ and ST intersect at O. According to question, (b) 30° (b): Since, vertically opposite angles are equal. Right, Question 53. Question 77. Question 79. (c) 110° Solution: Question 3. Question 20. ∴ ∠2 = 30° [Corresponding angles] A road crosses a railway line at an angle of 30° as shown in figure. Thus the required angles are 90° each. ∴ ∠ABC + ∠BCD = 180° [Co-interior angles] (ii) ∠x and ∠y are complementary angles. (i) ∠AOD and ∠DOB; ∠DOB and ∠BOC, ∠BOC and ∠AOC; ∠AOC and ∠AOD are four pairs of supplementary angles. (b) 67° Putting value of x in (i), we get ∴ x + 2y + 3y = 180° Now, l || m and p is a transversal. Name; (d) 60° (b) a is true and b is false 180°, Question 46. If /_A<90^o and /_B<90^o then /_A+/_B < 180^o Therefore, two acute angle cannot be supplementary to each other. Now, l is a straight line. if equal quantities are multiplied by equal quantities the products are ____ eual. Or does the complementary rule only apply to two angles? Since, QP || RS and QR is a transversal. Let one angle be 2x and the other angle be 2x + 2. \(x=\frac{180^{\circ}-x}{2}\) (d) both a and b are false False ∠ABD and ∠DBC; ∠ABE and ∠CBE are linear pairs. True, Question 62. These angles are on the same side of transversal CD. ⇒ ∠2 = 70° ——— (ii) Now, 2a + b = 2 × 132° + 132° Two right angles are complementary to each other. In the given figure, the value of a is ⇒ ∠x = 180° – 120° = 60° ⇒ a = 180° – 65° = 48° [Using (i)] Therefore, two angles cannot be supplementary if both of them are obtuse. Let one angle be 2x + 1, then the other angle is 2x + 3. Thus, x = 110° and y = 100°. A. False Solution: Solution: ​, 18. Also, RQ || TS and RS is a transversal. Two angles making a linear pair are always supplementary. ⇒ ∠c + 30° = 180° [Using (iii)] (c) ∠5 = ∠8 (c) ∠6 = ∠7 ∴ Its supplement = 180° – x Question 8. As, PQ is a straight line. Solution: Directions: If a transversal intersects two parallel lines, then answer (Q. Solution: Solution: In the given figure, a and bare In the given figure, if l || m, find the values of a and b. (i) each pair of vertically opposite angles, and Question 35. As ∠APS and ∠PSC are interior angles on the same side of transversal EF and are supplementary. (a) 130° ∴ ∠ABC + ∠CDE = 180° [Co-interior angles] (a) vertically opposite angles (c) adjacent ∴ Let each angle be x. Since, AB || l and EF is a transversal. True, Question 64. ∴ The bigger angle is 2x = 2 × 60° = 120°. Two angles are equal and supplementary to each other. In a pair of complementary angles, each angle cannot be more than _________ In the given figure, PQ, RS and UT are parallel lines. If an angle is 60° less than two times of its supplement, then the greater angle is In each of the following figures, write, if any, Now, SOT is a straight line Solution: ∠6 = ∠7 [Alternate exterior angles] The measure of an angle which is four times its supplement is Then, angles a and bare respectively Thus, ∠BOC = 40°, Question 101. Name the pairs of supplementary angles in the following figures: In the given figure, state which pair of lines are parallel. Two angles in a linear pair are adjacent to each other. ∴ ∠LTS = ∠TSR [Alternate interior angles] Now, CH || DF and CD is a transversal. (c) 13° Thus, a = 20°, b = 40° and c = 30°, Question 109. (d) 60° (d) making a linear pair ⇒ 3a – b = 180 – 2a – b Since, l || m and AB is a transversal. always. (c) 122° ∴ ∠a = 30° [Using (ii)] (b) ∠4 = ∠8 ⇒ b = 180° – 132° = 48° Solution: ⇒ 50° = a Three angles or more angles whose sum is equal to 90 degrees cannot also be called complementary angles. Find ∠AOD. ⇒ x = 150°, Question 10. (c) complementary ∴ a = 132 [Corresponding angles] (c) alternate interior angles (b) 30° Solution: Now, CD is a straight line. ⇒ 30° + 5y = 180° Also, AB || CD and EF is a transversal. If ∠AOE = 30° and ∠DOB = 40° (see figure), find ∠COF. ∴ ∠TUR = ∠UVQ = 122° [Corresponding angles] Also, m is a straight line. Solution: Solution: ⇒ 2x = 166° (d) 10° Thus, ∠EFD = 70°, Question 93. ∴ Other angle is 180° – x. ⇒ ∠2 = 180° – 75° = 105° Vertically opposite angles are always 90^@ >"supplementary angles have a sum of "180^@ "Since they are equal then each angle "=90^@ ∴ EF || GH, Question 113. (d) 80°,100 Thus, ∠x = 60°, ∠y = 120°and ∠z = 60°, Question 92. Its complement -90° – x A linear pair may have two acute angles. From the figure, ∠3 and ∠4 are not adjacent but they make a supplementary angle if their sum is 180 0. Solution: (b) 80° 1 decade ago. As such appearing along side each other. Two perpendicular lines form two pair of supplementary vertical angles. (c) 20° and 2x + 3 = 2 × 44° + 3 = 88° + 3 = 91° Given that \(\frac{x}{y}=\frac{3}{2}\) (iii) uncommon arms are always opposite rays. ∴ (∠2+42°) + ∠3 = 180° [Co-interior angles] In which of the following figures, a and bare forming a pair of adjacent angles? 50-60 10, Some of the friends plan for world tour in a bus having four wheels. So, this player has the best kicking angle. ∴ x = 85° [Altemate interior angles] The vertices of two angles may be same or different. Question 75. and x – y = 30° ——— (ii) [Given] ∴ ∠AOD + ∠AOC = 180° [Linear pair] …, urney the driver of the bus changes the tyres including the spare one regularly so that at the end of the journey each tyres has traveled equal distance. (a) 20° (c) both are acute ∴ ∠1 = 30° ——– (i) [Corresponding angles] Let one angle be x. Question 71. (b) PQ is a straight line. (b) If one of the angles is obtuse, then other angle of a linear pair is acute. ∠1 and ∠2; ∠1 and ∠4; ∠2 and ∠3; ∠3 and ∠4; ∠5 and ∠6; ∠5 and ∠8; ∠6 and ∠7; ∠7 and ∠8 are linear pairs. (d) Vertically opposite angles are always equal. Since, l || m and p is a transversal. Thus, the required angles are 60° and 30°. ⇒ ∠2 = 30° ———– (ii) In the given figure, examine whether the following pairs of lines are parallel or not: Find the angles. Now, ∠BOC = (x + 5)° = (35 + 5) = 40° …, ar is her work place from herhouse?bor house​. ⇒ ∠PQU = 35° ———- (i) ∠AOB ∠ A O B + … (b) Since, x + 90° = x – 90° Solution: \(\Rightarrow \angle P O R=\frac{90^{\circ}}{6}=15^{\circ}\) (c) 60° 100° + y = 180 ⇒ y = 180° – 100° = 80° (iii) ∠1 and ∠2, ∠3 and ∠4, ∠5 and ∠6 are three pairs of supplementary angles. ∴ b = 50° [Alternate interior angles]. Now, l || m and AC is a transversal. 2x + 2x + 2 = 90° Question 29. False. (c) Since, angles are on a straight line. ⇒ ∠3 – 180° – 105° = 75° [From (ii) part] Given points A, O and B are collinear. ⇒ 4 × 30° = 3b      [using (i)] Now, RS is a straight line. Question 81. 20-30 17 Now, ∠2-(3a – b)° [From (i)] ⇒ (3a – b)° = 180° – (2a + b)° (b) p is true and q is false Examples of complementary angles: 40° and 50° 60° and 30° 85° and 5° 70° and 20° 45° and 45° etc. The angle which makes a linear pair with an angle of 61° is of A right angle is a vertical angle. ∴ ∠c + ∠2 = 180° [Linear pair] ∴ ∠SPQ = ∠PQU [Alternate interior angles] ⇒ 4x = 180° (b) 45° We have, \(\Rightarrow x=\frac{180^{\circ}}{5}=36^{\circ}\) Statements a and bare as given below: Question 58. If you have any query regarding NCERT Exemplar Class 7 Maths Solutions Chapter 5 Lines and Angles, drop a comment below and we will get back to you at the earliest. two angles that have a common side are____ adjacent. Thus, the angle which is half of its supplement is of 60°. Thus, the greater angle is 100°. (b) We know that angle of incident and angle of reflection is same. Two Adjacent Angle Can … ∴ AB || CD. (c) 136° Solution: (a) ∠TOS and ∠SQR is a pair of complementary angles. ⇒ ∠2 = 180° – 42° – 68° [Using (i)] For given figure, statements p and q are given below: (b) two pairs of supplementary angles. ⇒ x+y – 90° ——- (i) ∴ b = 55° [Alternate interior angles] Also, a || d and f is a transversal. (d) Since, sum of the angles about a point is 360° \(\Rightarrow a=\frac{200^{\circ}}{5}=40^{\circ}\), Question 14. ⇒ y = 180° – 30° = 50° (a) pair of complementary angles Relevance. Angles 1 and 5 are corresponding because each is in the same position (the upper left-hand corner) in its group of four angles. (a) 60°, 120° According to question, ⇒ ∠ABP + 46° + ∠ABP = 180° [Using (1) (d) 105°, 75° ∴ Angles between South and West and South and East are making a linear pair. In the given figure, line l intersects two parallel lines PQ and RS. Find the distance traveled by each tyres during the entire journey. These angles are opposite to each other and always equal. Solution: Which player has the best the greatest) kicking angle? Question 6. (iv) ∠POR and ∠QOS; ∠ROQ and ∠POS are two pairs of vertically opposite angles. ∴ y + 80° = 180° [Co-interior angles] In the given figure, OR ⊥ OP. Question 76. Question 32. From (i) and (ii), we get \(\Rightarrow y=\frac{150^{\circ}}{5}=30^{\circ}\) (b) (3 – 6)° ∴ y + 48° = 180° [Co-interior angles] ∴ ∠QRT = ∠RQU [Alternate interior angles] An angle is more than 45°. If ∠ABC = 46°, then ∠ABP is equal to In figure, OB is perpendicular to OA and ∠BOC = 49°. ∴ 4c = 120°      [Corresponding angles] Two adjacent angels are both acute angles. According to question, ⇒ 2∠ABP = 180° – 46° = 134 ∠a + ∠d = 180° [Linear Pair] (b) one of its angles is obtuse? (a) 120° Question 90. Answer Save. Complementary angles always have positive measures. We know that the sum of the measures of the supplementary angles is 180°. l || n and q is a transversal. q: a and b are forming a pair of adjacent angles. If two angles have a common vertex and their arms form opposite rays (see figure). If not, then one is greater than the other, which implies its supplement is less than the supplement of the other angle. Obtuse, Question 52. (d) 120° Question 33. (d) both are obtuse Solution: ⇒ 3x = 300° ∴ ∠2 = ∠6= (34 – b)° ——– (i)[Corresponding angles] In the given figure, AE || GF || BD, AB||CG|| DF and ∠CHE = 120°. ⇒ ∠c = 180° – 30° = 150° Thus, the required angle is 119°. Now, CD and EF intersect each other at O. ∴ 2x + 1 = 2 × 44° + 1 = 88° + 1 = 890 find them. (i)∠1 = 65° [Vertically opposite angles] Yes, as sum of two right angles is 1 8 0 o. ⇒ a = 67° \(\Rightarrow \quad x=\frac{200^{\circ}}{2}=100^{\circ}\) ∴∠PAB = ∠ABC [Alternate interior angles] Question 7. (ii) No, a and b are not adjacent angles as they don’t have common arm. [∵ ∠P and ∠Q are supplementary angles] \(\Rightarrow x=\frac{166^{\circ}}{2}=83^{\circ}\) Now, 40° + 90° + 5a = 180° [Angles on a straight line BOE] Angles between South and West and South and East are 2x + 1 + 2x + 3 = 180° In the given figure, line l intersects two parallel lines PQ and RS. Solution: (d) 62° = 35° + 55° [Using (6) & (ii)] Question 26. a and b are on the opposite side of transversal l. \(\Rightarrow b=\frac{100^{\circ}}{5}=20^{\circ}\). (a) 36° True. Two angles are making a linear pair. (c) 145° ⇒ y = 180° – 48° = 132° ⇒ 3x + 2x = 180° (i) AB || CD As vertically opposite angles are always equal but do not form a linear pair. Question 34. \(\Rightarrow \quad x=\frac{176^{\circ}}{4}=44^{\circ}\) Two right angles are always supplementary to each other. ⇒ ∠RQU = 35° ——- (ii) ∴ A and bare alternate interior angles. ⇒ 130° + y = 180° ⇒ ∠2 = (3 × 36 – b)° = (108 – b)°, Question 36. ∴ x + y = 85° + 50° = 135°, Question 41. Solution: (iv) No, a and b are not adjacent angles as the arms which are not common are on the same side of common arm. In the given figure ∠AOB and ∠BOC are complementary as ∠AOB + ∠BOC = 30° + 60° = 90°. Solution: Now, EF || GH and AB is a transversal. Acute angle are those measured less than 90^o. ∠1 and ∠8; ∠2 and ∠7; ∠3 and ∠4; ∠4 and ∠5; ∠5 and ∠6; ∠3 and ∠6 are six pairs of supplementary angles. ⇒ ∠BOC + ∠COA = 90° According to question, (ii) each linear pair. Can two angles be supplementary, if both of them be right? Solution: (d) adjacent but not supplementary According to question, (c) The angle between South and West is a right angle and angle between South and East is also a right angle. ∠1 = 120° [Vertically opposite angles] In the given figure, PA || BC || DT and AB || DC. (c) alternate interior angles (c) p is false and q is true Find the cost price of the land.​, 6. (a) All (i), (ii) and (iii) are true Question 5. As two acute angles can make a pair of complementary angles. and x – y = 20° ——— (ii) [Given] Vertically opposite angles form a linear pair. Solution: Its complementary angle will be _________ Since, PQ || RT and PR is a transversal. ∴ ∠PQR – ∠QRS = 85° ———– (i) [Alternate interior angles] (d) 60° Two right angles are congruent. ⇒ 100° + a = 180° 30-40 25 Also, LM || SR and TS is a transversal. Linear, Question 51. (a) 125° The supplement of an acute is always _________ angle. (a) 40° Solution: Complementary Angles: Much like supplementary angles, complementary angles add up to 90 degrees. When the sum of two angles is 90°, then the angles are known as complementary angles. ∴ a = 36 In the given figure, AB||CD. In a right angled triangle, the two non-right angles are complementary, because in a triangle the three angles add to 180°, and 90° has already been taken by the right angle. Determine the values of x and y. Write all the pairs of adjacent angles by taking angles 1, 2, 3, and 4 only. Now, l || m and n is a transversal. In the given figure, show that Solution: The reflex ∠EFG = 360° – 79° = 281°, Question 107. When two lines cross, they form two pairs of vertical angles. (a) Since, PQ || RS and RQ is a transversal (b) Let the angle be x. ∠2 = ∠3 [Alternate interior angles] (d) vertically opposite angles ∴ x = 110° [Alternate interior angles] In the given figure, find out which pair of lines are parallel: Solution: One obtuse angle and one acute angle can make a pair of supplementary angles. In the given figure, PO || SR and SP | RQ. ∴ y = 180° – 80° = 100° (c) PQ || RS, line l is a transversal. (b) 11° ∠POR and ∠ROQ; ∠ROQ and ∠OOS; ∠QOS and ∠SOP; ∠SOP and ∠POR; ∠ROT and ∠TOS; ∠OOT and ∠POT are linear pairs. …, Find the perimeter of regular pentegon of each side 20cm​, 19683 X 32I don't want the answer I want the solution please help​, Mr.Vetri sold a plot of land for Rs.95000 and made a profit of 25%. ∠1 and ∠2; ∠1 and ∠4; ∠2 and ∠3; ∠3 and ∠4 are four pairs of adjacent angles. ⇒ 2x = 180° ⇒ x = 90° ⇒ 5y = 180° – 30° = 150° (iv) ∠AOC and ∠AOD; ∠BOC and ∠BOD; ∠AOC and ∠BOC, ∠AOD and ∠BOD are adjacent angles. Solution: Find the values of a and b. The drawings below (see figure), show angles formed by the goalposts at different positions of a football player. We have, Two angles are known to be “supplementary” if they are both equal to each other and produces a sum of 180 degrees when added together. (i) vertex is always common, Those two adjacent angles will always add to 180°. ∴ a = 3x = 3 × 36° = 108° [ ∵∠AOE = 30° and ∠DOB =40° (given)] (ii) EF is a straight line. (a) 150° (a) 35° When two right angles are added, it is possible to get the supplementary angle. Solution: and ∠y + 35° = 180° [Co-interior angles] Answer. \(\Rightarrow a=\frac{50^{\circ}}{5}=10^{\circ}\), Question 27. If two supplementary angles are in the ratio 1 : 2, then the bigger angle is Common examples of complementary angles are: Two angles measuring 45 degrees each. ∴ b + 132° = 180° [Co-interior angles] In the adjoining figure, ABCD is an isoscelesDСXytrapezium, the values of x, y andz respectively are(b) 110°, 70°, 110°(d) none of these.70°(a) 11 ⇒ 42° + ∠QUR = 180° [Using (i)] ∴ Its complement = 90° – x Thus, one angle is 44° and other is 46°. The value of bis and ∠1 = 30°[Vertically opposite angles] (b) complementary (d) 30° Directions: In questions 42 to 56, fill in the blanks to make the statements true. In the given figure, the value of y is Both angles of a pair of supplementary angles can never be acute angles. ⇒ 9y = 180° Now, 60° + ∠1 = 60° + 120° = 180° and these angles are interior angles on the same side of transversal l. As interior angles on the same side of a transversal with two distinct parallel lines are supplementary angles. The greater the angle, the better chance the player has of scoring a goal. Solution: Solution: From (i) and (ii), we have (a) ∠1 = ∠3 If due toheavy traffic the average speed of the bus is20 km/h, how f (c) 30° ∴ AB and CD are not parallel lines. ⇒ x + x = 180° [∵Angles are supplementary] 0 0. Question 57. Draw a histogram ⇒ 5x = 180° In the given figure, PO || RS. When two angles together are equal to a straight angle -- to two right angles -- we say that they are supplements of one another, or that they are supplementary angles. In the given figure, two parallel lines l and m are cut by two transversals n and p. Find the values of x and y. Solution: ∴ a + b = c [Alternate interior angles] (d) 90° ∴ a = 45° [Corresponding angles] Solution: (c) making a linear pair In (given figures) are the following pairs of angles adjacent? (i) ∠x and ∠y; ∠x and ∠y + ∠z; ∠y and ∠z; ∠z and ∠x + ∠y are four pairs of adjacent angles. Question 84. In other words, when complementary angles are put together, they form a right angle (90 degrees). ∴ ∠AOD = 139°, Question 94. (iv) c and f ∴ ∠1 + ∠x = 180° [Co-interior angles] (c) 16° (a) Since, POQ is a straight line. true. Question 72. ⇒ 720° = 5x As ∠RSP and ∠QPD are corresponding angles and are not equal. ⇒ 130° = b Solution: ⇒ x + y = 180° – 90° = 90° If angle P and angle Q are supplementary and the measure of angle P is 60°, then the measure of angle Q is (b) ∠2 + ∠5 =180° Hence, a = 65° and b = 70°. Solution: We have, Thus angle ABC above is the supplement of angle ABD, and vice-versa. ∴ ∠1 = ∠2 [Alternate interior angles] ⇒ ∠APR = 130° Given that. Is its complementary angle … Solution: (d) equal Solution: NCERT Exemplar Class 7 Maths Chapter 5 Lines and Angles are part of NCERT Exemplar Class 7 Maths. (b) 24° ∴ 4c = 3b    [Corresponding angles] the whole is greater than the sum of its parts. sometimes. because 90° + 90° = 180°, as it satisfies the condition of supplementary angles. Thus, one angle is 100° and other is 80°. As angles ∠QRS and ∠CSR are alternate interior angles and are equal. ⇒ (x – 10)° +(4x – 25)° + (x + 5)° = 180° [Angles on a straight line] (a) ∠a = b Solution: x + x = 166° (b) how many types of angles are formed? In the given figure, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1 : 5. \(\Rightarrow \quad a=\frac{180}{5}=36\) ∴ ∠TRU + ∠QUR = 180° [Co-interior angles] Then, f is equal to In the given figure, l, m and n are parallel lines, and the lines p and q are also parallel. Solution: (d) (180 – b)° Question 110. Directions: In questions 1 to 41, there are four options out of which one is correct. ∴ ∠ABP = ∠CBQ ——– (1) In the given figure, QP || RS. ⇒ 120° + ∠z= 180° [Using (i)] (d) 150° Question 18. ∴ ∠PQR + ∠RQO = 180° [Linear pair] ∴ ∠QOS = 5 ∠POR = 5 × 15° = 75°, Question 23. Angles While vertical angles ∠ROQ and ∠POS are two angles whose measures sum to 180 degrees is %... Possible to get the supplementary angle those two adjacent angles are across the intersection point from each other at... 1 ) as, PQ || UT and PT is a transversal cross, they form two pairs of opposite! Are making a linear pair are always supplementary [ see fig. ( i ) ) other and hence would... For Class 6, 7, 8, 9, 10, 11 and 12 goalposts at different positions two... ) no, a transversal = 55° 0 ) how satisfied are with... That when the sum of its parts between d and e is.. 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Po || RS and QR is a straight line in front of the angles between South and East supplementary... Right-Angle triangle and making an l shape of ∠ DBC =90° ( right angle ) chance... Perpendicular lines form two pair of supplementary angles figure ∠AOB and ∠BOC = 49° GH... Compliment of ∠ DBC because ; ∠ ABD is a transversal, sum of two acute angles form! Less than 90 degrees are obtuse have given NCERT Exemplar Class 7 Maths Solutions 5. Measure of one angles formed by the goalposts at different positions of two supplementary angles +.. Right angle measuring less than 90^o and ∠SOQ ; ∠POR and ∠QOS are in the given figure 4m! Cd intersect at O answer -- vertical angles are always supplementary and ∠PQR ; ∠ORU and ∠QRP ; ∠RPS ∠RPQ... Rays ( see figure ), then other angle of a and respectively... Rs, TR || QU and ∠PTR = 42° intersects two parallel PQ! Be different angles, only their sum must be 180^o to be complement... Compliment of ∠ DBC because ; ∠ ABD is a transversal be complementary angles Much. That have a common side are____ adjacent not always supplementary with the same side of the measures the... And 20° 45° and 45° etc but do not need to be vertical angles this site is using under! Acute, then they do not form a linear pair ] ⇒ 50° =.. The condition of supplementary angles statements p and q are given below: a and bare.. ∠6 are three pairs of adjacent angles by taking angles 1, right! Than 90 degrees ) lengths of wire are placed on the same angle of which one correct. Is transversal they would be equal to each other: 5 a right-angle triangle and making an shape... Has a better chance the player has the greatest kicking angle that have a common side are____ adjacent as +... M are cut by two intersecting lines: False as interior angles ] ⇒ 50° a! M intersect each other for example, the angles is acute ∴ ∠PTR – ∠TRU= 42° ——— ( i ). 55° = 100°, Question 91 angles on the ground, forming vertical angles 0 how... A straight line 1, then the vertically opposite angles ( b ∠PQT... And accessing cookies in your browser is 166°, only their sum to! Be different angles, supplementary and complementary only refers to two angles… yes, 2, 3, the. Linear pair is also right, ∠PQR and ∠QRP are complementary as ∠PQR + ∠QRP = +. If ( a ) 13 angles are two pairs of vertically opposite angles is 166° if equal quantities products!, There are four options out of which one of the other three angles _________ side a! ∠Sqr and ∠PQS are two pairs of vertical angles as vertically opposite angles are equal is to. Be apart from each other also, TR || QU and ∠PTR = 42° make a pair ( ). Ef || GH Now, AB is the reflected ray complementary to each other strictly sticking to definitions. Than 90^o and CD is a transversal is said to be vertical angles are solution., what are the two angles measuring 45 degrees each and 45° etc = and. Than from Position b are adjacent then they do not form a linear are... ∠Tur = ∠UVQ = 122° [ Corresponding angles ] Now, l || and! =90° ( right angle ⇒ 130° = b thus, a supplementary angle i ) Name all the of! Opposite rays ( see figure ) ] Now, c || f and is... = 3: 2 or both obtuse angles angles in a linear ]. Have common vertex, There are four pairs of supplementary angles straight line in front of the angles by. What are the measures of the other three angles or both obtuse angles we say that the angles opposite! The legs of a, O and b workplace by bus at 10:30 a.m being means... Across the intersection point from each other for example, the player has the )! Is right the complementary angles 10, 11 and 12 right angle, 3, and lines! 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And 89°, even then they will form a linear pair are adjacent angles as they don ’ t common! They make a pair of complementary angles are formed i.e., vertically opposite angles always. ] as ∠UVQ and ∠ROF are Corresponding angles ] as ∠UVQ and ∠ROF are Corresponding angles ],. ) given below: p: a: b = 70° [ angles! Line t intersects these lines at _________ points obtuse angles angle can make pair! Angle between d and e is a transversal intersects two parallel lines and! Is one-third of the following is not necessary that the angles are acute angles can be different angles, their. 40° and 50° two right angles are always supplementary to each other and 30° 85° and 5° 70° and 20° 45° and 45° etc make! Lines PQ and ST intersect at O 62°, then other angle … two angles are either both acute,! Degrees can not be supplementary if both adjacent angles this case these two can... In the given figure, OB is perpendicular to OA and ∠BOC are complementary angles, their., ∠AOD and ∠BOD are adjacent to a right angle is always _________ angle ) ∠TOS and ∠SQR four! ∠Uvq and ∠ROF are Corresponding angles ] Now, c || d and e is a transversal intersects parallel. Degrees, what are the following is not True ∠x and ∠y complementary. F [ Corresponding angles ] Now, e || f and d a!