(ii). If two angles have a common vertex and their arms form opposite rays (see figure). ⇒ ∠z = 180° – 120° = 60° ∴ a = 45° [Corresponding angles] janaeaholloway janaeaholloway 05/06/2019 Mathematics Middle School Use the diagram to identify the special angle pairs. l || m and PQ is a transversal ⇒ 3x = 180° 2.Two angles that form a linear pair are always supplementary. Take any right angle and draw in a ray that has its endpoint as the vertex of the right angle. ⇒ (x – 10)° +(4x – 25)° + (x + 5)° = 180° [Angles on a straight line] If one of them is one-third of the other, find the angles. Now, l is a straight line. ⇒ (3a + 5)° + (2a-25)° = 180° (b) one of its angles is obtuse? Now, LM || QP and QT is a transversal. (e) Since, POQ is a straight line. Thus, ∠BOC = 40°, Question 101. Question 28. (a) Since, PQ || RS and RQ is a transversal Answer: No. ∴ Its supplement = 180° – x ∴ ∠BCD = ∠CDT [Alternate interior angles] ∴ x + y = 90° ———(i)     [Angles are complementary] and b = 132° [Vertically opposite angles] ⇒ ∠ABC = 180° – 120° [Using (ii)] (b) 135° The measure of an angle which is four times its supplement is Solution: \(\Rightarrow x=\frac{180^{\circ}}{5}=36^{\circ}\) ∴ ∠SPQ = ∠PQU [Alternate interior angles] Give reason. (ii) There is no pair of vertically opposite angles. Find the values of a, b and c. a and b are on the opposite side of transversal l. Linear, Question 51. ⇒ ∠PQU = 35° ———- (i) 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: The Right angles can make a pair of complementary angles- _________, there have been several thefts in the houses in your locality. Solution: True. Its complement -90° – x ⇒ d = 180°- 38° = 142° [Using (i)] ⇒ x + y = 180° – 90° = 90° From (i) and (ii), we have When two right angles are added, it is possible to get the supplementary angle. Maths MCQs for Class 7 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. (a) 4th player has the greatest kicking angle. Solution: In the given figure, two parallel lines l and m are cut by two transversals p and 4. Now, ∠BOC = (x + 5)° = (35 + 5) = 40° (iv) No, a and b are not adjacent angles as the arms which are not common are on the same side of common arm. ⇒ (3a – b)° = 180° – (2a + b)° ∴ x + y = 180° ———– (i) ⇒ 3x + 2x = 180° And that is because their measures add up to 90 degrees. ∴ Its complement = 90° – x False. Since, AB || l and EF is a transversal. 2x + 1 + 2x + 3 = 180° 4.Two angles that are right are always congruent. As angles ∠QRS and ∠CSR are alternate interior angles and are equal. ∴ x + 64° + 46° +100° – 360° Question 7. Solution: Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees (right angle). ∴ ∠1 = 34° [Alternate interior angles] Question 35. ∠ABD and ∠DBC; ∠ABE and ∠CBE are linear pairs. Question 86. ∴∠PAB = ∠ABC [Alternate interior angles] And just as another point of … ∴ EF || GH, Question 113. Solution: In the given figure, l || m || n. ∠OPS = 35° and ∠QRT = 55°. ∴ ∠1 = 30° ——– (i) [Corresponding angles] Try These: Question 1: Which pairs of following angles are complementary? Since, l || m and q is a transversal Two angles form a linear pair. (b) ∠d=∠c (d) 144° - one angle is 90° and all three add up to 180°. ⇒ ∠2 = 30° ———– (ii) (a) 60°, 120° 2 See answers profantoniofonte profantoniofonte Answer: … (c) alternate interior angles When talking about complimentary angles, always remember that the angles appear in pairs. (a) Botha and bare true Solution: We have, (a) Since, ∠P + ∠Q = 180° Find the angles. and ∠1 = 30°[Vertically opposite angles] From (i), (a) 120° Solution: A road crosses a railway line at an angle of 30° as shown in figure. Solution: A right angle measures 90°. ⇒ 85° + a = 180° [Using (ii)] (a) vertically opposite angles Example 2: 60°+30° = 90° complementary and adjacent Example 3: 50°+40° = 90° complementary and non-adjacent (the angles do not share a common side). ∵ AB is a straight line. In the given figure, find the value of ∠BOC, if points A, O and B are collinear. ⇒ 2∠ABP = 180° – 46° = 134 Solution: If ∠x = ∠y = ∠z, then ∠x and ∠y; ∠y and ∠z; ∠z and ∠x are three pairs of complementary angles. Thus, ∠COF = 110°, Question 95. Complementary angles are pair angles with the sum of 90 degrees. Let one angle be 2x and the other angle be 2x + 2. (a) 36° 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. Solution: Solution: (a) 125° Thus, one angle is 44° and other is 46°. Question 75. Since  ∠AOC and ∠BOC have a common vertex O, a common arm OC and also, their non-common arms, OA and OB, are opposite rays. Solution: C. an acute angle. Solution: Solution: Such angle pairs are called a linear pair. Let one angle be x. (b) 50°,130° (b) 30° We have, Solution: Now, CD is a straight line. a: If two lines intersect, then the vertically opposite angles are equal. Also, m is a straight line. Solution: Question 85. because 90° + 90° = 180°, as it satisfies the condition of supplementary angles. Knowledge of the relationships between angles can help in determining the value of a given angle. We have, (a) Since, POQ is a straight line. (a) 120° Let one angle be x and other be y. ∠1 +∠2 = 180° [Angles on a straight line PQ] Since, l || m and is a transversal. Since, angles are supplementary ∠1 and ∠8; ∠2 and ∠7; ∠3 and ∠4; ∠4 and ∠5; ∠5 and ∠6; ∠3 and ∠6 are six pairs of supplementary angles. Vertically opposite angles form a linear pair. Let one angle be 2x + 1, then the other angle is 2x + 3. Complementary Angles. (c) ∠3 + ∠8 = 180° According to question, ∴ ∠3=68° ——– (i) [Corresponding angles] 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 … Solution: No, two acute angles cannot form a pair of supplementary angles. (d) 80°,100 45° : Given, angle = 45° ∴ ∠b + ∠1 = 180° [Linear pair] (i) ∠x and ∠y; ∠x and ∠y + ∠z; ∠y and ∠z; ∠z and ∠x + ∠y are four pairs of adjacent angles. (c) 150° (c) making a linear pair In a right triangle, the two smaller angles are always complementary.(Why? Name; ∴ ∠PTR – ∠TRU= 42° ——— (i) [Alternate interior angles] ∴ 6a = 120° [Corresponding angles] In the given figure, AB || CD, AF || ED, ∠AFC = 68°and ∠FED = 42°. Solution: Since, PQ || RT and PR is a transversal. (c) p is false and q is true Each one of these angles is called the Complementary of the other. We know that when the measure of an angle is exactly 90°, then it is known as a right angle. x = 4 (180° – x) (c) 13° 3.Two angles that are congruent are sometimes right. ∴ 2x = 2 × 22° = 44° and 2x + 2 = 44° +2 = 46° Supplementary Angles. Solution: How do you think about the answers? Solution: (c) The angle between South and West is a right angle and angle between South and East is also a right angle. In the given figure, PQ||RS and a : b = 3 : 2. Question 74. In the given figure, if QP || SR, the value of a is They can be adjacent angles but don’t have to be. (i) AB || CD (a) Let the angles be x and y. (i) ∠1 and ∠3; ∠2 and ∠4; ∠5 and ∠7; ∠6 and ∠8 are four pairs of vertically opposite angles. ⇒ ∠b = 180° – 30° = 150° [Using (1)] Thus, ∠EFD = 70°, Question 93. One angle is complementary to the other or One angle is the complement of the other. (a) 110° ⇒ ∠BCD = 180°- 50° = 130° Thus, the required angle is 119°. (i) b and c Solution: As if both angles are 89° and 89°, even then they cannot make the sum 180°. Solution: ∴ ∠x = 35° [Alternate interior angles] ∴ b = 70° [Corresponding angles] ∴ ∠AOE + ∠EOD + ∠DOB = 180° (a) 95°, 85° If ∠POR = 90° and x : y = 3 : 2, then z is equal to Solution: Thus, the angle which is half of its supplement is of 60°. ⇒ ∠ABP + 46° + ∠ABP = 180° [Using (1) Vertically opposite angles are always Adding (i) and (ii), we get ∴ AB || CD. ⇒ 130° + y = 180° (c) m and n are two straight lines and I is a transversal intersecting both lines m and n. Yes, because the sum of two angles is 180, and if they are both 90 degrees, they add up to 180, making them supplementary, and of the same measure, making them congruent. Parallel, Question 50. Also, PQ || RS and line I is a transversal. Question 32. . Solution: In the given figure, if AB || CD, ∠APQ = 50° and ∠PRD = 130, then ∠QPR is (∵ 45° + 45° = 90° and 60° + 30°= 90°). ∴ a + b = c [Alternate interior angles] (a) 36° ∴ Other angle is 180° – x. False sum of interior angles on the same side of a transversal is _________ Solution : False Measure of right angle is 90°. One obtuse angle and one acute angle can make a pair of complementary angles. Question 79. In Parts (a) and (b) given below, it may help to trace the diagrams and draw and measure angles. (b) 108° Now, RS is a straight line. (c) 100°, 60° (d) ∠a = ∠b [Vertically opposite angles] (a) 20° Measures (in degrees) of two complementary angles are two consecutive even integers. Question 68. ADC and BDC are . Solution: (d) 120° ⇒ 50° + ∠BCD = 180° Question 67. ⇒ 3x = 180° – x ⇒ 3x + x = 180° ∴ ∠POR + ∠ROS + ∠QOS = 180° Free PDF Download of CBSE Maths Multiple Choice Questions for Class 7 with Answers Chapter 5 Lines and Angles. ∴ x + 2x = 180° (b) complementary In the given figure, POQ is a line. So, the sum of two right angles = 90° + 90° = 180°. ∴ x = 110° [Alternate interior angles] (d) ∠2 + ∠3 = 180° You can check whether an angle is a right angle by using a set square, like in the picture below. ⇒ ∠EOD = 180° -30° – 40° = 110° ——— (i) (a) 10° (iii) No, a and b are not adjacent angles as they don’t have common vertex. (b) Since, x + 90° = x – 90° ∴ 4c = 120°      [Corresponding angles] Solution: (b) 67° Question 73. (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. Question 21. (b) 61° Hence, two right angles are never be complementary. 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