## 24 يناير two right angles can make a pair of complementary angles

Since, AE || BD and CH is a transversal. Also, m || n and p is transversal. From (i) and (ii), we get (d) 119° ⇒ 130° = b (b) 50° Explanation: Angle equal to 90 o is called right angle. Solution: (c) ∠6 = ∠7 ∴ y = 180° – 80° = 100° How do you think about the answers? In the given figure, state which pair of lines are parallel. In figure, OB is perpendicular to OA and ∠BOC = 49°. Solution: \(\Rightarrow \quad k=\frac{90^{\circ}}{5}=18^{\circ}\) Complementary angles are two angles that have a sum of 90°. ∴ b + d = 180° [Co-interior angles] Thus, ∠BOC = 40°, Question 101. In the given figure, the value of x is ∠1 = 120° ———- (i) [Vertically opposite angles] Adding (i) and (ii), we get If ∠x = ∠y = ∠z, then ∠x and ∠y; ∠y and ∠z; ∠z and ∠x are three pairs of complementary angles. According to question, (a) ∠1 = ∠5 (a) 29° (d) both are obtuse In the given figure, PO || RT. (d) 60° (c) 136° Question 74. We know that when the measure of an angle is exactly 90°, then it is known as a right angle. (a) ∠a = b Solution: The value of a is Since, l || m and is a transversal. 1 answer. (a) alternate exterior angles Hence, a = 65° and b = 70°. Solution: Question 112. ∠EPQ+ ∠GQP = 130° + 50° = 180° add up to 90 degrees(a Right Angle ). ⇒ (3a – b)° = 180° – (2a + b)° Since, QP || RS and QR is a transversal. Thus, ∠x = 60°, ∠y = 120°and ∠z = 60°, Question 92. (a) 60°, 30° \(x=\frac{1}{3}\left(180^{\circ}-x\right)\) Solution: When talking about complimentary angles, always remember that the angles appear in pairs. (c) 90° Right, Question 53. Which of the following is false? Question 8. Question 3: Can two right angles complement each other? \(\Rightarrow c=\frac{120^{\circ}}{4}=30^{\circ}\) ———– (i) Now, 2a + b = 2 × 132° + 132° In the given figure, P, Q and R are collinear points and TQ ⊥ PR, ADC and BDC are . (i) ∠1 and ∠3; ∠2 and ∠4; ∠5 and ∠7; ∠6 and ∠8 are four pairs of vertically opposite angles. (d) supplementary Measures (in degrees) of two supplementary angles are consecutive odd integers. Now, EF || GH and AB is a transversal. Question 1. Solution: In the given figure, line l intersects two parallel lines PQ and RS. (d) 144° Two angles are Complementary when they. Online protractor or angle problems with acute, obtuse, reflex angles. (b) We know that angle of incident and angle of reflection is same. ∴ ∠QOS = 5 ∠POR = 5 × 15° = 75°, Question 23. Now, l is a straight line. In Parts (a) and (b) given below, it may help to trace the diagrams and draw and measure angles. Complementary angles are those whose sum is equal to 90°. Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees (right angle). (ii) Let the angle between d and e is ∠2. (a) 100° ⇒ 9y = 180° ∴ Other angle is 180° – x. A + B = 90° Question 66. Question 75. ∴ ∠ABP + ∠ABC + ∠CBQ = 180° (c) 60° According to question, In the figure above, the two angles ∠ PQR and ∠ JKL are complementary because they always add to 90° Often the two angles are adjacent, in which case they form a right angle.. We hope the NCERT Exemplar Class 7 Maths Chapter 5 Lines and Angles will help you. In the given figure, line I intersects two parallel lines PQ and RS. If the sum of measures of two angles is 180° then they are _________ Solution: These two are supplementary because. Also, ∠EFG = ∠1 + ∠2 – 34° +45° = 79° 180°, Question 46. ∴ EF || GH, Question 113. In the given figure, show that If ∠AOE = 30° and ∠DOB = 40° (see figure), find ∠COF. Name the pairs of supplementary angles in the following figures: (b) Statement a is true but statement b is false since, if a transversal intersects two parallel lines, then the sum of two interior angles on the same side of the transversal is 180°. Solution: An acute angle measures greater than 0° and less than 90°. A right angle measures 90°. A linear pair may have two acute angles. Given that ∠AOB = 90° [∵ OB ⊥ OA] Solution: [ ∵∠AOE = 30° and ∠DOB =40° (given)] Question 30. (b) ∠2 = ∠4 So, the sum of two right angles = 90° + 90° = 180°. Here we have given NCERT Exemplar Class 7 Maths Solutions Chapter 5 Lines and Angles. Solution: \(\Rightarrow a=\frac{50^{\circ}}{5}=10^{\circ}\), Question 27. ⇒ x = 150°, Question 10. Thus, ∠ABC = 60° and ∠CDE = 120°, Question 100. Two right angles are complementary to each other. (b) one of its angles is obtuse? D. a supplementary angle. (b) 80° Now, PQ || RS and PR is a transversal. Now, AB || DC and BC is a transversal. Use the diagram to identify the special angle pairs. ∴ x + 2x = 180° ∴ Its complement = 90°- 45° = 45°, Question 56. ∠2 = ∠4 [Corresponding angles] Solution: ∴∠CHE = ∠HCB – 120° ———- (i) [Alternate interior angles] 2.Two angles that form a linear pair are always supplementary. The reflex ∠EFG = 360° – 79° = 281°, Question 107. Adding (i) and (ii), we get Question 61. Statements a and bare as given below: Solution: Solution: (a) Botha and bare true Question 33. \(\Rightarrow \quad x=\frac{210}{6}=35\) ⇒ a = 180° – 65° = 48° [Using (i)] Solution: \(\Rightarrow x=\frac{120^{\circ}}{2}=60^{\circ}\) Therefore the two smaller ones must add to 90° and so are complementary by definition). Solution: ⇒ x + y = 180° – 90° = 90° (a) 60°, 120° Two angles form a linear pair. ∴ b = 55° [Alternate interior angles] c || f and a is transversal. ∠1 +∠2 = 180° [Angles on a straight line PQ] Solution: EASY. Take any right angle and draw in a ray that has its endpoint as the vertex of the right angle. (b) 11° ADC and BDC are . ⇒ 5b – 180° – 80° = 100° Find ∠EFD. Find each of the angles. ∴ ∠ABP = ∠CBQ ——– (1) ∠1 and ∠8; ∠2 and ∠7; ∠3 and ∠4; ∠4 and ∠5; ∠5 and ∠6; ∠3 and ∠6 are six pairs of supplementary angles. ∴ ∠a = 30° [Using (ii)] 3.Two angles that are congruent are sometimes right. Reflex Angle. Question 5. Solution: Now, l || m and p is a transversal. ∴ a = 36 False Distinct. ⇒ ∠ABP + 46° + ∠ABP = 180° [Using (1) (d) 45°, 45° True, Question 65. We know that the sum of the measures of the complementary angles is 90° ∴ 6y + y + 2y = 180° \(\Rightarrow \angle P O R=\frac{90^{\circ}}{6}=15^{\circ}\) These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°: Notice that together they make a straight angle. (d) Let the angle be x. Solution: Find the sum 2a +b. (d) 80° Solution: Give reason. As angles ∠QRS and ∠CSR are alternate interior angles and are equal. Solution: ∴ ∠COF = ∠EOD = 110° [Using (i)] [Vertically opposite angles] Since, a transversal intersects two parallel lines, then interior angles on the same side of a transversal are supplementary. In the given figure, l || m || n. ∠OPS = 35° and ∠QRT = 55°. (a) 4th player has the greatest kicking angle. (b) corresponding angles (d) both p and q are false One of the complementary angles is said to be the complement of the other. (iv) ∠AOC and ∠AOD; ∠BOC and ∠BOD; ∠AOC and ∠BOC, ∠AOD and ∠BOD are adjacent angles. ∴ ∠2 = 30° [Corresponding angles] \(\Rightarrow x=\frac{720^{\circ}}{5}=144^{\circ}\), Question 16. Yes, 2 right angles can form a supplementary angle. You can specify conditions of storing and accessing cookies in your browser. (c) 145° ∴ ∠POR + ∠ROQ = 180° [Linear pair] Also, AB || CD and EF is a transversal. Solution: (b) 45° Recall that the complementary angle is one that makes the given angle become 90°. (a) ∠1 = ∠3 ∴ ∠AOD = 139°, Question 94. What is the type of other angle of a linear pair if ⇒ x + 2x = 300° (a) ∠TOS and ∠SQR is a pair of complementary angles. Solution: Then Since, 90° + 90° = 180°, a supplementary angle. Thus, the required angle is 119°. If the complement of an angle is 799, then the angle will be of Opposite, Question 49. Find ∠AOD. What is the measurement of the other angle? ⇒ 4x = 90° – 2 = 88° (b) Let the angle be x. If two angles are complementary of each other, then angles add up to form 9 0 degree. ∴These angles are supplementary. 4.Two angles that are right are always congruent. Solution: ∴ (∠2+42°) + ∠3 = 180° [Co-interior angles] From (i), The angle which makes a linear pair with an angle of 61° is of (iv) Let the angle between c and fig ∠4. ∴ ∠BCD = ∠CDT [Alternate interior angles] Question 21. Solution: They just need to add up to 90 degrees. (c) 30°, 50° ∠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. Solution: Since, l || m and AB is a transversal. Question 45. If the sum of two angles is 180 degrees then they are said to be supplementary angles, which forms a linear angle together.Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together. ∠POR + 5 ∠POR = 90° Thus, m || n as the sum of co-interior angles is 180°. ∴ ∠AOE + ∠EOD + ∠DOB = 180° Thus, the greater angle is 100°. Solution: ∴ ∠2 + 75° = 180° [Co-interior angles] It will produce the same result. Solution: Question 26. (a) Seven football players are practicing their kicks. (i) AB || CD Linear, Question 51. Question 86. Since, two angles form a linear pair. (i) ∠AOD and ∠DOB; ∠DOB and ∠BOC, ∠BOC and ∠AOC; ∠AOC and ∠AOD are four pairs of supplementary angles. In the given figure, PQ||RS and a : b = 3 : 2. ∴ ∠QRS – ∠TSR = 85° ———- (ii) [Using (i)] [Alternate interior angles] and its supplement = 180° – x= 180°- 100 = 80° Find the reflex ∠EFG. It is just a complete one angle. ⇒ ∠RQU = 35° ——- (ii) (c) making a linear pair Question 73. Sum of two right angles is 180° which is double the sum of two complementary angles. Question 80. Question 59. and ∠y + 35° = 180° [Co-interior angles] Question 110. The sum of two vertically opposite angles is 166°. We have, (c) Draw a line L.M passing through T such that LM || QP || SR. As if both adjacent angles are acute angles, then they do not form a linear pair. Question 34. A pair of complementary angles is angl… Get the answers you need, now! Use on interactive whiteboards, angles can be automatically shown or measured with a protractor. Proof (a) All (i), (ii) and (iii) are true In the given figure, PA || BC || DT and AB || DC. ⇒ a = 180° – 100° = 80°. Solution: (i) Since, PQ || UT and PT is a transversal. Hence, ∠x = 35° and ∠y = 145°. Now, ∠2-(3a – b)° [From (i)] …, y. write a letter to the editor of the local newspaper describing the incident and drawing the attention of the police to the need for better night patrolling, 3) Hasthe growth of worldot worn population,contribute to thebad environments situation today, what impact has the interview with arun krishnamurthy made on you, what is the meaning of e cash and explain the, Ram said to me,"Don't forget what I told you", (d) The book isthe table. Three lines AB, CD and EF intersect each other at O. Both angles of a pair of supplementary angles can never be acute angles. Solution: Solution: \(\Rightarrow \quad a=\frac{180}{5}=36\) (d) (180 – b)° One obtuse angle and one acute angle can make a pair of complementary angles. ⇒ ∠z = 180° – 120° = 60° Thus, ∠EFD = 70°, Question 93. (b) Since, x + 90° = x – 90° Therefore, B will be less than 45°. 45 to 48). According to question, So, this player has the best kicking angle. Question 29. In the given figure, QP || RS. In this construction you can extend either leg back. Solution: Two angles are making a linear pair. Each one of these angles is called the Complementary of the other. janaeaholloway janaeaholloway 05/06/2019 Mathematics Middle School Use the diagram to identify the special angle pairs. (d) 22.5° (c) 85° (c) 110° (ii) There is no pair of vertically opposite angles. (b) 15° (b) 90°, 90° (b) making a linear pair Thus, one angle is 44° and other is 46°. (b) 144° a: If two lines intersect, then the vertically opposite angles are equal. ⇒ 3x = 180° – x ⇒ 3x + x = 180° In the given figure, lines PQ and ST intersect at O. 2x + 2x + 2 = 90° What is a Complementary Angle? Since, angles are supplementary Now, p || q and n is a transversal. Thus, a = 20°, b = 40° and c = 30°, Question 109. Then, f is equal to Complementary angles are any two angles that sum to 90°. ∵ AB is a straight line. ⇒ B = 90° – A What is the measurement of the other angle? In the given figure, find the value of ∠BOC, if points A, O and B are collinear. ∴ Its complement = 90° – x ⇒ ∠2 = (3 × 36 – b)° = (108 – b)°, Question 36. Solution: ∴ x + y = 90° ———(i) [Angles are complementary] (c) 36° (a) interior angles on the same side of the transversal (b) 135° We have divided the right angle into 2 angles that are "adjacent" to each other creating a pair of adjacent, complementary angles. (c) 20°, 50° Students can solve NCERT Class 7 Maths Lines and Angles MCQs Pdf with Answers to know their preparation […] \(\Rightarrow a=\frac{200^{\circ}}{5}=40^{\circ}\), Question 14. ∴ ∠4 = 75° [Alternate interior angles], Question 91. As two right angles are supplementary to each other. Solution: ⇒ ∠AOD = 180°- 41° [Using (1)] As one acute angle and one obtuse angle can make two supplementary angles. If the two complementary angles are adjacent then they will form a right angle. If ∠1 = (2a + b)° and ∠6 (3a – b)°, then the measure of ∠2 in terms of b is ∴ ∠1 = ∠3 = 30° ——— (ii) [Corresponding angles] In the given figure, PO || RS, TR || QU and ∠PTR = 42°. If the complement of an angle is 62°, then find its supplement. (d) Since, x – 10° + 190°- x = 180° In (given figures) are the following pairs of angles adjacent? (b) 30° Let A and B are two angles making a complementary angle pair and A is greater than 45° ⇒ 50° + ∠BCD = 180° ⇒ ∠ABC = 180° – 120° [Using (ii)] If two angles add up to 90°, they are _____ angles. NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12. (ii) AB and CD Question 81. Write down each pair of adjacent angles shown in the following figures: (a) pair of complementary angles Find the angles x and y. Solution: You can check whether an angle is a right angle by using a set square, like in the picture below. (c) 45° True, Question 69. In the given figure, POQ is a line, then a is equal to ⇒ 4 × 30° = 3b [using (i)] Easy measure angles, using interactive whiteboard angle simulator. Question 78. = 35° + 55° [Using (6) & (ii)] ∴ 6a = 120° [Corresponding angles] False ⇒ d = 180°- 38° = 142° [Using (i)] (b) 50°,130° When talking about complementary angles, it's important to remember that they're always in apair. From (i) and (ii), we have (a) 95°, 85° Complementary angles are two angles whose measures add to 90°. Now, a + b = 180° [Angles on a straight line PQ] ∴ ∠1 = 30° ——– (i) [Corresponding angles] The C in complementary can be used to form the 9 in 90. The S in supplementary can be used to form the 8 in 180. Now, 40° + 90° + 5a = 180° [Angles on a straight line BOE] Question 67. In the given figure, PQ || ST. Then, the value of x + y is Supplementary angles and complementary angles are defined with respect to the addition of two angles. One angle is the complement of the other angle. One obtuse angle and one acute angle can make a pair of complementary angles. Question 32. (b) two pairs of supplementary angles. These 2 angles (∠AOB and ∠AOC) are Complementary Angles, because they add up to 90° (30°+60°). Let x = 3k and y – 2k Solution: Acute, Right, Obtuse, Straight, Reflex & Complete angle. (d) 154° (d) We have, \(\Rightarrow x=\frac{180^{\circ}}{5}=36^{\circ}\) Same, Question 48. Its complementary angle must be less than 45°. Question 7. One obtuse angle and one acute angle can make a pair of supplementary angles. ∴ x + 66° = 180° [Co-interior angles] Give reason in support of your answer. Then, ∴∠PAB = ∠ABC [Alternate interior angles] The greater the angle, the better chance the player has of scoring a goal. ∴ AB || CD. ∴ 4c = 120° [Corresponding angles] ∴ ∠2 + 3 = 180° [Co-interior angles] Question 71. ⇒ 3x = 180° So an angle of 30° has a supplementary angle of 90° - 30° = 60°. b: If a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is 180°. (b) Since, PA || BC and AB is a transversal. ⇒ ∠2 = ∠y = 120° [Vertically opposite angles] Solution: - one angle is 90° and all three add up to 180°. (a) 120° Now, l || m and AC is a transversal. In which of the following figures, a and bare forming a pair of adjacent angles? Solution: ∴ ∠TRU + ∠QUR = 180° [Co-interior angles] ⇒ 5a – 20° = 180° Complementary, Question 43. Solution: Thus, a = 67° and b = 48°, Question 102. The angle The angles x and 90° – x are ∠d = ∠c [Vertically opposite angles] The angles x – 10° and 190° – x are Since, l || m and q is a transversal. Now, e || f and c is a transversal. Solution: (d) 80°,100 Solution: Two angles making a linear pair are always supplementary. Question 72. If x= 30°, then ∠QOR is Solution: Vertically opposite angles form a linear pair. (a) 20° = 90°. Solution: Determine the values of x and y. (d) 10° ∴ x + y = 180° ———– (i) (c) 20° (d) adjacent but not supplementary ⇒ 42° + ∠QUR = 180° [Using (i)] \(\Rightarrow y=\frac{150^{\circ}}{5}=30^{\circ}\) When two right angles are added, it is possible to get the supplementary angle. Question 70. Question 25. Question 90. ∠FOR + ∠QRH = 123° + 57° = 180° (ii) each linear pair. Two supplementary angles always form a linear pair. ⇒ 2x + x = 180° So the measure of angle DBA plus the measure of angle ABC is equal to 90 degrees. ⇒ b = 180° – 132° = 48° Solution: Thus, one angle is 89° and other is 91°, Question 99. ⇒∠APQ + ∠QPR = 130° As ∠EPQ and ∠GQP are interior angles on the same side of transversal AB and are supplementary The difference of two complementary angles is 30°. In the given figure, if AB || CD, ∠APQ = 50° and ∠PRD = 130, then ∠QPR is False (c) The angle between South and West is a right angle and angle between South and East is also a right angle. ⇒ 60° + ∠2 = 180° [Using (ii)] ∴ Angles between South and West and South and East are making a linear pair. ∴ a = 45° [Corresponding angles] ⇒ ∠QPR = 130° – 50° = 80°, Question 11. In the given figure, the value of y is (d) 120° (c) 13° (c) 80° (c) 72° (b) 144° (iv) No, a and b are not adjacent angles as the arms which are not common are on the same side of common arm. (a) vertically opposite angles Complementary angles are pair angles with the sum of 90 degrees. ∴ Let a = 3x and b – 2x Solution: Obtuse, Question 52. They form a right angle when you add them up. ∴ a = 132 [Corresponding angles] Directions: In questions 42 to 56, fill in the blanks to make the statements true. Question 103. (i) EF and GH ∴ ∠1 + ∠z = 180° (Co-interior angles) If an angle is 60° less than two times of its supplement, then the greater angle is Thus, one angle is 45° and other is 180° – 45° = 135°, Question 98. Question 57. sum of interior angles on the same side of a transversal is _________ (b) 4th player has the greatest kicking angle. Question 24. Question 42. (c) Since, PQ || RS and line 1 is a transversal. ∴ x + y = 85° + 50° = 135°, Question 41. (ii) ∠x and ∠y are complementary angles. Solution: \(\Rightarrow \quad a=\frac{120^{\circ}}{6}=20^{\circ}\) What is the difference between supplementary angles and a linear pair? 0 0. and 2x + 3 = 2 × 44° + 3 = 88° + 3 = 91° In the given figure, AB||CD. ∴ ∠PTR – ∠TRU= 42° ——— (i) [Alternate interior angles] ∴ b = 50° [Alternate interior angles]. Complementary angles: Two angles that add up to 90° (or a right angle) are complementary. Question 87. Also, a || d and f is a transversal. If the sum of measures of two angles is 90%, then the angles are _________ Solution: ∴ a + b = c [Alternate interior angles], Question 106. Complementary Angles. ⇒ 720° = 5x Now, PQ || RT and RQ is a transversal. (b) 30° 4 years ago. (i) ∠PSC = ∠RSF = 50° [Vertically opposite angles] Solution: Find the values of a, b and c. Solution: (c) m and n are two straight lines and I is a transversal intersecting both lines m and n. Its complement -90° – x Let one angle be x and other be y. In a right angle triangle, as the measure of the right angle is fixed, the remaining two angles always form the complementary as the sum of … ∴ These angles are complementary. Find the values of a and b. In the given figure, PO || SR and SP | RQ. Now, CH || DF and CD is a transversal. Hence, ∠a = 30°, ∠b = 150°, ∠c = 150°. False ⇒ ∠x = 180° – 120° = 60° ⇒ x = 180° – 66° = 114° \(\frac{\angle P O R}{\angle Q O S}=\frac{1}{5}\) Find the measures of two complementary angles if one angle is five times the other angle. (c) 80 ⇒ (3a + 5)° + (2a-25)° = 180° Two lines AB and CD intersect at O (see figure). Solution: Two lines in a plane which do not meet at a point anywhere are called _________ lines. Then, which of the following is true? (i)∠1 = 65° [Vertically opposite angles] Solution: ⇒ 50° = a ⇒ x = 720° – 4x (a) ∠1 + ∠5 = 180° Solution: Solution: Given points A, O and B are collinear. ⇒ 5a = 180° + 20° = 200° ⇒ 3a – b = 180 – 2a – b ⇒ 3a – b + 2a + b = 180 ⇒ 5a = 180 ⇒ ∠y = 180° – 35° = 145° and b = 132° [Vertically opposite angles] a and b are on the opposite side of transversal l. Then, which one of the following is not true? ∴ ∠TUR = ∠UVQ = 122° [Corresponding angles] when the owners were awa (a) (2 + b)° (a) 30° ∴ ∠ABC + ∠BCD = 180° [Co-interior angles] 1. Parallel, Question 50. (b) ∠d=∠c Question 9. An angle is 45°. If one of them is one-third of the other, find the angles. Solution: ∴ ∠1 + ∠5 = 180° [By(i)and(iii)] (c) a is false and b is true ∠a + ∠d = 180° [Linear Pair] (d) Vertically opposite angles are always equal. But the angles don't have to be together. (d) 60° = 264° + 132° = 396°. In the given figure, write all the pairs of supplementary angles. ∠APS + ∠PSC = 130° + 50° = 180° ⇒ 5x = 180° We have, Help Amisha in finding the angles. If a transversal intersects two parallel lines, and the difference of two interior angles on the same side of a transversal is 20°, find the angles. ⇒ 5y = 180° – 30° = 150° ⇒ 4x = 180° Solution: (iii) ∠1 and ∠2, ∠3 and ∠4, ∠5 and ∠6 are three pairs of supplementary angles. The supplement of an obtuse angle is always _________ angle. ⇒ ∠2 = 180° – (2a+ b)° ——– (ii) [∵ ∠1 = (2a + b)° (given)] (ii) PQ || UT and PT is a transversal. 90°, Question 55. In a pair of complementary angles, each angle cannot be more than_____. Answer: No. Two adjacent angles always form a linear pair. (c) Since, angles are on a straight line. (a) supplementary Question 58. (a) 95° (a) 44° Interior angles on the same side of a transversal with two distinct parallel lines are complementary angles. ⇒ 30° + 5y = 180° Solution: Question 2. 0 0. erminia . Solution: ⇒ a = 180° – 85° = 95°. Recall that two angles are complementary if the sum of their measures is 90°. ⇒ ∠POR + ∠QOS = 180° – 90° = 90° ——- (i) The drawings below (see figure), show angles formed by the goalposts at different positions of a football player. 2 angles are Complementary when they add up to 90 o (a Right Angle). Question 89. (b) 61° Since, l || m and q is a transversal We have, Solution: (i) ∠x and ∠y; ∠x and ∠y + ∠z; ∠y and ∠z; ∠z and ∠x + ∠y are four pairs of adjacent angles. Question 22. Question 85. ⇒ 5a = 180° – 130° = 50° In the given figure, PQ is a mirror, AB is the incident ray and BC is the reflected ray. (a) Both statements p and q are true. Solution: (a) 40° Solution: alternate Interior angles are on the _________ side of the transversal. Since, AF || ED and FD is a transversal. (c) ∠a + ∠d = 180° Kyuvaraj1034 is waiting for your help. In the given figure, 4m and a line t intersects these lines at P and Q, respectively. (iii) uncommon arms are always opposite rays. The angles between North and West and South and East are False Supplementary Angles. ⇒ 60° + 20 = 180° Given that. ∴ AB and CD are not parallel lines. (c) (108 – b)° ⇒ ∠c = 180° – 30° = 150° ∴ x = 85° [Altemate interior angles] ⇒ ∠COA – 41° ——— (i) (a) 36° ⇒ 90° + x + y = 180° The legs of a stool make an angle of 35″ with the floor as shown in figure. (d) 30° ∴ b = 48° ——— (i) ∴ 2x + 1 = 2 × 44° + 1 = 88° + 1 = 890 (a) Let an angle be x. There's also a word for two angles whose sum add up to 90 degrees, and that is complementary. (d) supplementary angles ⇒ ∠2 = 180° – 75° = 105° ⇒ 6 ∠POR = 90° True. l || m and PQ is a transversal ∴ a = f [Corresponding angles] 82° _____ 5. Question 82. Also, m is a straight line. (c) adjacent In the given figure, examine whether the following pairs of lines are parallel or not: In the given figure, if PQ || RS and QR || TS, then the value of a is (c) 64° In the given figure, ∠AOC and ∠BOC form a pair of Three angles or … \(x=\frac{180^{\circ}-x}{2}\) (a) If one of the angles is acute, then other angle of a linear pair is obtuse. \(\Rightarrow \quad x=\frac{176^{\circ}}{4}=44^{\circ}\) Thus, x = 110° and y = 100°. (b) ∠PQT and ∠TOR; ∠SQR and ∠PQS are two pairs of supplementary angles. ∠a = ∠3 [Vertically opposite angles] As ∠APS and ∠PSC are interior angles on the same side of transversal EF and are supplementary. We have, (b) If one of the angles is obtuse, then other angle of a linear pair is acute. Solution: So we can also say that angles DBA and angles ABC are complementary. From (i) and (ii), we get Solution: (ii) EF || GH ⇒ 120° + ∠z= 180° [Using (i)] (d) 120° Solution: Now, a + b = 45° + 55° = 100°, Question 105. (c) 79° ∴ ∠3=68° ——– (i) [Corresponding angles] ⇒ 2∠ABP = 180° – 46° = 134 Question 20. ⇒ ∠COA = 90° – 49° [∵ ∠BOC = 49° (given)] (a) one of its angles is acute? Find ∠PQR. Which player has the best the greatest) kicking angle? We have, Justify your answer. (i) toon(iii)up, explain various security standards for internet. In the given figure, PQ, RS and UT are parallel lines. 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