Solution: 2. ⇒ d = 180°- 38° = 142° [Using (i)] ⇒ y = 90° – 60° = 30° ⇒ 4x = 90° – 2 = 88° True, as all the angles are right angles and the diagonals are congruent to each other. Parallel, Question 50. They have a common vertex. (vii) The diagonals of a trapezium, divide each other into proportional segments. A linear pair may have two acute angles. (d) 60° Now, 2a + b = 2 × 132° + 132° (d) 45°, 35° ⇒ 90° – 62° = x l || n and q is a transversal. true. Solution: False. An Interior Angle is an angle formed inside a geometric shape. ⇒ ∠BOC + ∠COA = 90° Question 8. Question 96. (c) 60° ∴ ∠1 = 34° [Alternate interior angles] 180°, Question 46. Answer: (b) complementary angles Hint: Definition of complementary angles ∵ AB is a straight line. (b) (3 – 6)° ⇒ x = 180° – 66° = 114° (b) two pairs of supplementary angles. Adding (i) and (ii), we get Now, EF || GH and AB is a transversal. Vertical angles are always congruent angles, so when someone asks the following question, you already know the answer. (b) PQ is a straight line. (a) Since, POQ is a straight line. ∴ ∠PQR + ∠RQO = 180° [Linear pair] Solution: In the given figure, line I intersects two parallel lines PQ and RS. Two angles are making a linear pair. a = d true. ∴ a = 3x = 3 × 36° = 108° Solution: (a) 20° ... the bisectors of vertical angles are opposite rays. ∠3 + ∠8 = 180° ——– (ii) [Co-interior angles] (d) 119° Which of the following statements is false? In the given figure, the value of a is Find ∠QUR. (c) ∠a + ∠d = 180° In the given figure, show that Given two parallel lines are cut by a transversal, their same side exterior angles are congruent. We have, Solution: ⇒ f = 108°, Question 37. Thus, 30 degree and 60 degree are written as 30° and 60° respectively. No, two acute angles cannot form a pair of supplementary angles. (b) 60° ∴ A and bare alternate interior angles. ∴ EF and GH are not parallel lines. It is also called semi-circular protractor. According to vertical angle theorem, in a pair of intersecting lines, the vertically opposite angles are equal. Answer: false. Find x. ∴ b + d = 180° [Co-interior angles] ⇒ ∠2 = 180° – 135° = 45° (a) 36° (ii) Name all the pairs of complementary angles. ⇒ x + 4x = 720° Theorem: In a pair of … In the given figure, PQ, RS and UT are parallel lines. Find the angles. ∴ ∠QOS = 5 ∠POR = 5 × 15° = 75°, Question 23. b: If a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is 180°. Always. Sum of the measure of an angle and its vertically opposite angle is always. ∴ Its supplement = 180° – x (a) 44° Solution: The two angles are supplementary angles. Write down each pair of adjacent angles shown in the following figures: Solution: (c) 30° Question 24. NCERT Exemplar Class 7 Maths Chapter 5 Lines and Angles are part of NCERT Exemplar Class 7 Maths. Q. ⇒ 5a = 180° – 130° = 50° (a) pair of complementary angles (d) 150° Both hands are at the same point in figure 1. Now, QP || RS and PR is a transversal. The measure of an angle which is four times its supplement is = 90°. ∴ ∠a = 30° [Using (ii)] Now, LM || QP and QT is a transversal. (c) 5° 60°: Let the angle be x. Solution: Now, a || d and c is a transversal. (d) ∠a = ∠d Line BC has been extended as line CD. b = e false. (d) In figure (d), a and bare adjacent angles since, they have a common vertex, common arm and also, their non-common arms are on either side of common arm. These angles are always equal to each other. (b) 100° (c) When a transversal cuts two parallel lines, each pair of interior angles on the same side of the transversal are supplementary. Solution: In the given figure, l, m and n are parallel lines, and the lines p and q are also parallel. ⇒ 90° + x + y = 180° (b) Since, POQ is a straight line Solution: Answer. A protractor has dual scales. ⇒ ∠COA = 90° – 49° [∵ ∠BOC = 49° (given)] Solution: (b) 30° \(\Rightarrow x=\frac{166^{\circ}}{2}=83^{\circ}\) This is the measurement of ∠ABC. Two angles forming a _________ pair are supplementary. Question 32. Question 112. Now, CD and EF intersect each other at O. In the given figure, PQ || ST. Then, the value of x + y is Hence, ∠a = 30°, ∠b = 150°, ∠c = 150°. Solution: Solution: Also, m is a straight line. The value of a is Solution: Note: They are also called Vertical Angles , which is just another way of saying the same thing. degree. C. This statement is true because a triangle cannot have two or more angles that are greater than 60°. 4. ⇒ ∠RQU = 35° ——- (ii) Putting value of x in (i), we get (d) Let the angle be x. Question 70. a = d true. Solution: ⇒ 100° + a = 180° but ∠4 ≠ ∠8, Question 38. The difference of two complementary angles is 30°. False Solution: (c) 79° (b) If one of the angles is obtuse, then other angle of a linear pair is acute. (b) complementary angles ⇒ a = 180° – 85° = 95°. ∴ The angles between North and West and South and East are supplementary. (c) 122° Solution: 2. true or false: planes are created by 3 collinear points. ∠a = ∠3 [Vertically opposite angles] ⇒ 60° + ∠2 = 180° [Using (ii)] ∴ Angles between South and West and South and East are making a linear pair. ⇒2x = 180° – x 300 seconds . ⇒ 6 ∠POR = 90° Question 67. (d) 62° One complete rotation of minute hand in one hour makes angle of ……. 60° + y = 90° ⇒ 120° + ∠x – 180° [Using (1)] Lines and Angles Class 7 MCQs Questions with Answers. Question 111. Answer: True. ∠ABD and ∠DBC; ∠ABE and ∠CBE are linear pairs. Question 80. Question 72. Question 6. (a) Seven football players are practicing their kicks. Two adjacent angles always form a linear pair. Answer: a = 140°, b = 40° and c = 140°. Thus, the required angle is 11°. If ∠POR = 90° and x : y = 3 : 2, then z is equal to Question 30. (a) alternate exterior angles True, Question 62. Arm, Question 47. ∴ EF || GH From (i) and (ii), we get Find the values of a and b. One obtuse angle and one acute angle can make a pair of complementary angles. The adjacent angles are the angles that have a common vertex. (iv) c and f (b): Since, vertically opposite angles are equal. (c) 55° Question 90. (a) 60°, 30° 45 to 48). ∴ ∠LTS = ∠TSR [Alternate interior angles] An angle that is greater than 180 degrees is called a reflex angle. Vertical Angles. When measuring an angle, the centre of the protractor is placed over the vertex (corner) B of the angle and the base line of the protractor is placed along one of the lines of the angle BC. (c) ∠3 + ∠8 = 180° Solution: Then, which one of the following is not true? ⇒ ∠x + ∠2 = 180° [Co-interior angles] Solution: b : If a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is 180 o . NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12. ∠1 +∠2 = 180° [Angles on a straight line PQ] In which of the following figures, a and bare forming a pair of adjacent angles? We have, and x – y = 30° ——— (ii) [Given] According to question, Corresponding Angles. ∴ 4c = 120°      [Corresponding angles] Vertical angles are formed by two intersecting lines. ∴ (a + b) + 65° = 180° [Co-interior angles] and x – y = 20° ——— (ii) [Given] ∴ ∠ABP + ∠ABC + ∠CBQ = 180° (c) 145° A transversal intersects two or more parallel lines. ∴ ∠c + ∠2 = 180° [Linear pair] ∴ ∠b + ∠1 = 180° [Linear pair] ⇒ 3x = 180° – x ⇒ 3x + x = 180° Thus, ∠x = 60°, ∠y = 120°and ∠z = 60°, Question 92. Two vertically opposite angles are always equal. (d) (ii) is false = 35° + 55° [Using (6) & (ii)] ∠1 and ∠8; ∠2 and ∠7; ∠3 and ∠4; ∠4 and ∠5; ∠5 and ∠6; ∠3 and ∠6 are six pairs of supplementary angles. Solution: (a) one of its angles is acute? Thus, ∠COF = 110°, Question 95. If the angles are adjacent to each other after the intersection of the lines, then the angles are said to be adjacent. The sum of the Interior Angle and the Exterior Angle are 360°. Which of the following is false? The common point is called its vertex of the angle. Solution: ∴ ∠1 + ∠x = 180° [Co-interior angles] Solution: (a) 130° ⇒ x = 360°- 210° Then, the values of a and bare respectively. ∴ ∠TRU + ∠QUR = 180° [Co-interior angles] True False: Q 2: Any two right angles are supplementary. According to question, So, this player has the best kicking angle. a : If two lines intersect, then the vertically opposite angles are equal. Right, Question 53. \(\Rightarrow \quad y=\frac{180^{\circ}}{9}=20^{\circ}\), Question 17. Solution: (a) Botha and bare true (d) 64° (b) Let the angle be x. True False: Q 3: Any two adjacent angles have a common vertex. Question 33. ... Property: If two lines intersect each other, then the vertically opposite angles are equal. ∴ b = 70° [Corresponding angles] Two lines in a plane which do not meet at a point anywhere are called _________ lines. If ∠β =120°, find value of ∠α. Answer. ⇒ 50° + ∠QPR – 130° It is denoted by °. ∴These angles are supplementary. Solution: There are three types of angles formed by parallel lines and a transversal. What is value of the supplementary angle of an angle measuring 75°? (c) adjacent Supplemental angles are those that, if positioned adjacent to each other, form a straight angle. (d) Vertically opposite angles are always equal. As two right angles are supplementary to each other. An Interior Angle is an angle inside the shape ABC. Thus, ∠EFD = 70°, Question 93. Solution: Thus, the greater angle is 100°. Opposite, Question 49. and 2x + 3 = 2 × 44° + 3 = 88° + 3 = 91° (a) 120° Acute, Question 54. Then, the angles are ∴ x + 2y + 3y = 180° The supplement of an obtuse angle is always _________ angle. (iv) ∠AOC and ∠AOD; ∠BOC and ∠BOD; ∠AOC and ∠BOC, ∠AOD and ∠BOD are adjacent angles. (b) 144° Question 29. (c) (i) is false but (ii) and (iii) are true 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. (a) 13 angles are formed. In the given figure, a = 40°. A + B = 90° \(\Rightarrow \quad a=\frac{180}{5}=36\) ⇒ 50° = a ⇒ x + y = 180° – 90° = 90° Solution: (i) Since, PQ || UT and PT is a transversal. ⇒ 30° + 5y = 180° A transversal intersects two or more than two lines at _________ points. Also, AB || CD and EF is a transversal. \(\Rightarrow \quad x=\frac{210}{6}=35\) Solution: Find the values of a, b and c. As if both angles are 89° and 89°, even then they cannot make the sum 180°. ∴ 2x + 1 = 2 × 44° + 1 = 88° + 1 = 890 (b) 75° (d) Since, sum of the angles about a point is 360° ∴ ∠QRT = ∠RQU [Alternate interior angles] Give reason. Now, SOT is a straight line Solution: and ∠1 = 30°[Vertically opposite angles] Find ∠PQR. true or false: through any two points, there exists only 1 line. Then, which of the following is true? Introduction to Point, Ray, Line and Line-Segment, Click to share on Facebook (Opens in new window), Click to share on Twitter (Opens in new window), Click to share on LinkedIn (Opens in new window), Click to share on Reddit (Opens in new window). a = ∠1 + ∠2 = 60° + 30° = 90°. (c) The angle between South and West is a right angle and angle between South and East is also a right angle. Since, PQ || RT and PR is a transversal. Let the angle be x. Two angles whose sum is  90 degrees are called Complementary Angles, Two angles whose sum is  180 degrees are called Supplementary Angles. (d) 101° Solution: ∴ 6y + y + 2y = 180° Also, m || n and QR is a transversal. Since, l || m and q is a transversal ⇒ 3a – b + 2a + b = 180 ⇒ 5a = 180 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. False Correct: The sum is 360°. Putting the value of x in (i), we get In the given figure, AB || CD, AF || ED, ∠AFC = 68°and ∠FED = 42°. (i) ∠AOD and ∠DOB; ∠DOB and ∠BOC, ∠BOC and ∠AOC; ∠AOC and ∠AOD are four pairs of supplementary angles. False In the given figure, PO || SR and SP | RQ. Angles may be classified based on their angle magnitude. Solution: An angle is generally named by three consecutive alphabets such as A, B and C or X, Y and Z. It has a base line at the bottom. Question 71. 4.if a transversal intersect two lines, alternate angles are equal. In the given figure, a and bare Question 25. Solution: Directions: If a transversal intersects two parallel lines, then answer (Q. These are corresponding angles, therefore they are equal. 4. The greater the angle, the better chance the player has of scoring a goal. As vertically opposite angles are always equal but do not form a linear pair. ⇒ 4x = 180° Example: Find angles a°, b° and c° below: Because b° is vertically opposite 40°, it must also be 40° A full circle is 360°, so that leaves 360° − 2×40° = 280° Angles a° and c° are also vertically opposite angles, so must be equal, which means they are 140° each. ⇒ ∠COA – 41° ——— (i) They could be complementary in a highly skewed parallelogram in which one angle is 45 degrees. ⇒ ∠RSC = 180° – 65° = 115° (d) Since, x – 10° + 190°- x = 180° Solution: a: If two lines intersect, then the vertically opposite angles are equal. ∴ ∠APR = ∠PRD [Alternate interior angles] The angle measures the amount of turn between the two arms two and is usually measured in degrees or radians. The side of a triangle that is opposite an angle greater than or equal to 180 is always the largest side of the triangle. (b) 4th player has the greatest kicking angle. (ii) ∠PQT and ∠PQR; ∠ORU and ∠QRP; ∠RPS and ∠RPQ are adjacent angles. Solution for Fill in the blank/s: True or false: A triangle in which two sides and an angle opposite one of them are given (SSA) always results in at least one… ∴ ∠ABC + ∠BCD = 180° [Co-interior angles] (i) Let the angle between b and c is ∠1. (ii) Every rhombus is a rectangle. Both angles of a pair of supplementary angles can never be acute angles. 1. (b) complementary angles. Also, AB || DF and BD is a transversal. Solution: (iii) Angles … (ii) Let the angle between d and e is ∠2. (d) A transversal cuts two … (a) 35° (ii) No, a and b are not adjacent angles as they don’t have common arm. ⇒ (6x – 30) = 180 ⇒ 6x – 180 + 30 = 210 In one particular case, when vertical angles are right … (i) ∠1 and ∠3; ∠2 and ∠4; ∠5 and ∠7; ∠6 and ∠8 are four pairs of vertically opposite angles. Now, l || m and AC is a transversal. 25 and 65. ∴ ∠AOD + ∠AOC = 180° [Linear pair] \(\Rightarrow y=\frac{150^{\circ}}{5}=30^{\circ}\) Solution: Now, 60° + ∠1 = 60° + 120° = 180° and these angles are interior angles on the same side of transversal l. 9. ⇒ ∠EOD = 180° -30° – 40° = 110° ——— (i) In the diagram below, state the angles that are vertically opposite to one another and are equal in measure . Solution: (False) (vi) 30° is one-half of its complement. \(\Rightarrow x=\frac{300^{\circ}}{3}=100^{\circ}\) The legs of a stool make an angle of 35″ with the floor as shown in figure. In the given figure, PO || RS, TR || QU and ∠PTR = 42°. ∠POR + 5 ∠POR = 90° Solution: (a) supplementary The angles in a complete turn add up to 360 degrees. From (i) and (ii), we get Let x = 3k and y – 2k ∴ Its complement = 90°- 45° = 45°, Question 56. 2. (d) Since PQ I RS and line 1 is a transversal. The two angles α (alpha), and β (beta) are vertically opposite angles and so α = β, Question 5: Find the complement of angle 45°, Sum of two complement angles are 90°. Hence, a = 65° and b = 70°. Solution: (c) m and n are two straight lines and I is a transversal intersecting both lines m and n. (d) 45°, 45° Two right angles are complementary to each other. ∴ ∠RST + a = 180° [Linear pair] (c) 90° Solution: In a pair of complementary angles, each angle cannot be more than _________ One complete rotation makes a circle and forms the maximum angle. In each of the following figures, write, if any, (b) 11° ∴ ∠AOD = 139°, Question 94. Since, 90° + 90° = 180°, a supplementary angle. In the given figure, state which pair of lines are parallel. Question 66. (b) a is true and b is false Find the value of a + b. \(x=\frac{1}{3}\left(180^{\circ}-x\right)\) (b) 15° ⇒ y = 180° – 30° = 50° (b) Let the angle be x. ∴ ∠SPQ = ∠PQU [Alternate interior angles] As can be seen from the figure above, when two lines intersect, four angles are formed.Each opposite pair are called vertical angles and are always congruent.The red angles ∠ JQM and ∠ LQK are equal, as are the blue angles ∠ JQL and ∠ MQK. (c) 110° (a) Let the angles be x and y. False Now, RS is a straight line. Solution: (i) False (ii) True (iii) True (iv) False (v) True (vi) True (vii) True 12. Therefore, Page No 10.16: Question 17: In the given figure, a is greater than b by one third of a right-angle. alternate Interior angles are on the _________ side of the transversal. If one complete rotation is divided into 360 equal parts, the measure of each such part is one degree or 1°. ⇒ ∠2 = 30° ———– (ii) in a plane, the relation "is perpendicular to" is transitive. Thus, the required angle is 119°. According to question, ⇒ b = 180° – 132° = 48° Solution: ∴ a = 132 [Corresponding angles] (ii) ∠POS and ∠SOQ; ∠POR and ∠ROQ are two pairs of supplementary angles. (d) equal Since, AE || BD and CH is a transversal. The angles that are opposite are called "vertical" angles. In the given figure, PA || BC || DT and AB || DC. Now, CH || DF and CD is a transversal. z + y = 180° [Linear pair] Also, ∠EFG = ∠1 + ∠2 – 34° +45° = 79° In the given figure, if l || m, find the values of a and b. ∠1 = ∠2 ——– (iii) [Verticallyopposite angles] Question 84. (c) complementary In the above example of clock, the two hands initially make smallest angle 0° and on one complete rotation by the minute hand, the two hands make maximum angle and is named as the angle 360 degree or 360°. (a) interior angles on the same side of the transversal 90°, Question 55. a: If two lines intersect, then the vertically opposite angles are equal. Solution: (a) Let an angle be x. ∴ ∠POR + ∠ROQ = 180° [Linear pair] \(\Rightarrow a=\frac{50^{\circ}}{5}=10^{\circ}\), Question 27. As ∠EPQ and ∠GQP are interior angles on the same side of transversal AB and are supplementary From (i), (b) 15° In the diagram below the two angles α (alpha), and β (beta) are vertical angles and α = β In the diagram below the two angles α (alpha), and β (beta) are vertical angles and α = β. ⇒ 60° – ∠L ——— (i) (b) 50°,130° ∴ x = 110° [Alternate interior angles] Now, l is a straight line. Your email address will not be published. In the given figure, PO || RT. True, Question 69. The size of an angle depends on the extent of rotation. According to question, \(\Rightarrow \quad x=\frac{176^{\circ}}{4}=44^{\circ}\) Which of the following statements are true (T) and which are false (F)? Question 73. Solution: Solution: A full rotation consists of four right angles. For this example, I suggest a horizontal line. Solution: ⇒ 120° + ∠z= 180° [Using (i)] Solution: If an angle is 60° less than two times of its supplement, then the greater angle is (a) 100° (b) 80° (c) 60° (d) 120° 35. (d) 60° Solution: ∴ x + y = 90° ———(i)     [Angles are complementary] (b) Given that a : b = 3 : 2 Let A and B are two angles making a complementary angle pair and A is greater than 45° (i) Every parallelogram is a rhombus. Thus, one angle is 44° and other is 46°. (b) 125° (a) Since, PQ || SR and RP is a transversal Two angles that have a common vertex and opposite to each other formed by the same two lines are called vertically opposite angles. How many degrees are in a “straight angle”? Also, a vertical angle and its adjacent angle are supplementary angles, i.e., ... For a pair of opposite angles the following theorem, known as vertical angle theorem holds true. \(\Rightarrow a=\frac{200^{\circ}}{5}=40^{\circ}\), Question 14. Solution: Solution: In the given figure, 4m and a line t intersects these lines at P and Q, respectively. (b) corresponding angles Its complementary angle must be less than 45°. Two angles that have a common vertex and opposite to each other formed by the same two lines are called vertically opposite angles. Since, l || m and is a transversal. ∴ The bigger angle is 2x = 2 × 60° = 120°. ⇒ 42° + ∠QUR = 180° [Using (i)] \(\Rightarrow x=\frac{180^{\circ}}{3}=60^{\circ}\) a and b are on the opposite side of transversal l. ⇒ 2∠ABP = 180° – 46° = 134 In the given figure, ∠AOC and ∠BOC form a pair of \(\Rightarrow \quad k=\frac{90^{\circ}}{5}=18^{\circ}\) l || m and QR is a transversal. On a picture below angles #/_KML# and #/_KMH# are supplemental since together they form a straight angle #/_LMH#.. ∠FOR + ∠QRH = 123° + 57° = 180° Note: A vertical angle and its adjacent angle is supplementary to each other. Find the angles. Solution: \(\Rightarrow x=\frac{720^{\circ}}{5}=144^{\circ}\), Question 16. ∴ a + b = c [Alternate interior angles] (d) ∠3 = ∠7 State with reasons whether the following statements are ‘true’ or ‘false’. ∴ a = 36 ⇒ ∠b = 180° – 30° = 150° [Using (1)] ⇒ 5 ∠POR = ∠QOS ——– (ii) ∴ ∠PQR – ∠QRS = 85° ———– (i) [Alternate interior angles] 2x + 1 + 2x + 3 = 180° If two angles have a common vertex and their arms form opposite rays (see figure). Question 104. Solution: \(\Rightarrow \quad x=\frac{88^{\circ}}{4}=22^{\circ}\) ∴ ∠2 + ∠5 = 180° —— (i) [Co-interior angles] Angles a° and c° are also vertically opposite angles, so must be equal, which means they are 140° each. True (vii) The diagonals of a parallelogram bisect each other at right angles. True, Question 64. (Vertical angles such as ... Then one of the alternate angles is an exterior angle equal to the other angle which is an opposite interior angle in the triangle. Solution: If two supplementary angles are in the ratio 1 : 2, then the bigger angle is Solution: ⇒ ∠y = 180° – 35° = 145° If angle P and angle Q are supplementary and the measure of angle P is 60°, then the measure of angle Q is Can two obtuse angles form a … Solution: As ∠β =120°, ∠ α = 180-120 = 60°. A reflex angle is greater than 180 degrees. Solution: (d) 135° Let us measure an angle with the help of a protractor. Parallel lines are always the same distance apart, and are indicated using arrow symbols. (See blue line). (a) both p and q are true ⇒ ∠ABC = 180° – 120° [Using (ii)] Solution: \(\frac{\angle P O R}{\angle Q O S}=\frac{1}{5}\) Question 2. So, this player has the best kicking angle. Question 19. First, if a transversal intersects two lines so that corresponding angles … Solution: In Fig. (iv) Let the angle between c and fig ∠4. In the given figure, PQ||RS and a : b = 3 : 2. \(\Rightarrow c=\frac{120^{\circ}}{4}=30^{\circ}\) ———– (i) (a) ∠TOS and ∠SQR is a pair of complementary angles. (ii). (i) EF and GH ∴ Its supplement = 180° – x Question 76. Answer: a = 140° , b = 40° and c = 140° . [∵ ∠P and ∠Q are supplementary angles] The diagonals of a quadrilateral_____bisect each other. Thus, the angle which is half of its supplement is of 60°. Vertical Angles: Theorem and Proof. ⇒ 130° = b Question 21. ∴ Other angle is 180° – x. ∴ y + 48° = 180° [Co-interior angles] Amisha makes a star with the help of line segments a, b, d, e and f, in which a || d, b || e and c || f. Chhaya marks an angle as 120° as shown in figure, and asks Amisha to find the ∠x, ∠y and ∠z. Vertical Angles are a pair of nonadjacent anglesopposite each other formed when two lines cross.Vertical angles are two angles opposite of each other. Now, PQ || RS and PR is a transversal. SURVEY . (d) making a linear pair An angle is a figure formed by two rays meeting at a common point. Solution: (i)∠1 = 65° [Vertically opposite angles] Find the measure of the segment. (c) 70°, 110° 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. The diagram below shows a protractor. Solution: STUDY. ∴ x + 66° = 180° [Co-interior angles] True or false. Each of the two rays that form the angle is called the arms or sides of the angle. Now, CD is a straight line. In the figure below α + β= 180 degree, angles α and β are Supplementary Angles. (a) ∠1 + ∠5 = 180° We have, Since, AB || l and EF is a transversal. (d) 30° Question 61. ∠ACD +30° = 90° ∴ AB || CD (c) 80 ∴ ∠PTR – ∠TRU= 42° ——— (i) [Alternate interior angles] Greek letters like α (alpha), β (beta) or θ (theta) are generally used as the symbols for the measured value of an angle. One has a measure of 6x - 2 and the other has a measure of 3x + 4. In the given figure, lines and m intersect each other at a point. 2x = 180° + 20° = 200° ⇒ 3x + 2x = 180° [ ∵∠AOE = 30° and ∠DOB =40° (given)] Solution: The two vertically opposite angles are always equal. ⇒ 9y = 180° As ∠RSP and ∠QPD are corresponding angles and are not equal. Question 89. Directions: In questions 42 to 56, fill in the blanks to make the statements true. ⇒ 5x = 180° and ∠y + 35° = 180° [Co-interior angles] Hence ∠ACD and ∠DCB are complementary angles. Here we have given NCERT Exemplar Class 7 Maths Solutions Chapter 5 Lines and Angles. The reflex ∠EFG = 360° – 79° = 281°, Question 107. Question 18. ∴ ∠BCD = ∠CDT [Alternate interior angles] Geometry Finals Semester 1 Always, Sometimes, Nevers. Two lines will meet in one point only when they are parallel. Let one angle be 2x + 1, then the other angle is 2x + 3. Write the correct one. (d) 80° ⇒ ∠x = 180° – 120° = 60° ⇒ a = 67° (d) 90° (c) both are acute Question 87. (a) Let the two angles be x and 2x. (iii) ∠TSV and ∠USV; ∠SVT and ∠SVU are adjacent angles. ∴ ∠TUR = ∠UVQ = 122° [Corresponding angles] ∴ ∠x = 35° [Alternate interior angles] (c) 150° Solution: Obtuse, Question 52. In figure, OB is perpendicular to OA and ∠BOC = 49°. (b) Since, PQ || ST and SO is a transversal. but ∠2 + ∠3 = 180°, Question 39. An angle which is half of its supplement is of ∴ (b) 90°, 90° (a) 10° (a) If one of the angles is acute, then other angle of a linear pair is obtuse. (c) vertically opposite Comment document.getElementById("comment").setAttribute( "id", "a45dd83c58a54e8143debfefdf41bd5a" );document.getElementById("da6c1f75c6").setAttribute( "id", "comment" ); © MathsTips.com 2013 - 2021. ∴ ∠QOR = 3y = 3× 30° = 90°, Question 15. Then, which one of the following is not true? Also, BC || DT and DC is a transversal. In the given figure, l || m || n. ∠OPS = 35° and ∠QRT = 55°. ⇒ ∠2 = (3 × 36 – b)° = (108 – b)°, Question 36. 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