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vertically opposite angles are always equal true or false

(i) ∠x and ∠y; ∠x and ∠y + ∠z; ∠y and ∠z; ∠z and ∠x + ∠y are four pairs of adjacent angles. . 3.adjacent supplementary angles form a linear pair. Write the correct one. A + B = 90° ⇒ y = 90° – 60° = 30° If ∠β =120°, find value of ∠α. Generally false. (b) 15° ⇒ 85° + a = 180° [Using (ii)] ⇒ 120° + ∠x – 180° [Using (1)] True False: Q 5: If two lines are perpendicular to each other, then all the pairs of vertically opposite angles formed are supplementary. (b) Given that a : b = 3 : 2 Now, a || d and c is a transversal. In (given figures) are the following pairs of angles adjacent? Thus, one angle is 45° and other is 180° – 45° = 135°, Question 98. Two angles forming a _________ pair are supplementary. (d) 45°, 35° \(\frac{\angle P O R}{\angle Q O S}=\frac{1}{5}\) In the given figure, PO || RT. ∴ Supplement of x = 180° – 28° = 152°, Question 88. Solution: Which of the following statements are true (T) and which are false (F)? (b) 135° If they were supplementary, they would not be vertical angles. The magnitude of the angle is the amount of rotation of one arm about the vertex to reach to the position of the second arm. (d) 120° Draw two crossing lines. ⇒ 5x = 180° \(\Rightarrow \angle A B P=\frac{134^{\circ}}{2}=67^{\circ}\). ∠a = ∠3 [Vertically opposite angles] Answer: false. We know that the sum of the measures of the complementary angles is 90° True or false. (b) two pairs of supplementary angles. (ii) EF || GH If ∠x = ∠y = ∠z, then ∠x and ∠y; ∠y and ∠z; ∠z and ∠x are three pairs of complementary angles. You can see that they can never share a side and be adjacent, so clearly this is false. ∴ x + 66° = 180° [Co-interior angles] Two right angles are always supplementary to each other. The Exterior Angle is the angle between a side of a shape AC, and the extended line CD. Thus, x = 110° and y = 100°. degree. (d) (180 – b)° ∴ x + y = 90° ———(i)     [Angles are complementary] (b) 100° ⇒ 60° + ∠2 = 180° [Using (ii)] Corresponding Angles. Find the values of a and b. (d) We have, Right, Question 53. (a) vertically opposite angles Thus, one angle is 44° and other is 46°. ⇒ x + x = 180° [∵Angles are supplementary] 90° – x = 62° \(\Rightarrow \angle P O R=\frac{90^{\circ}}{6}=15^{\circ}\) BUT, these angles are not supplementary, as they don't always complete eachother. \(\Rightarrow \quad x=\frac{176^{\circ}}{4}=44^{\circ}\) (b) Since, PQ || ST and SO is a transversal. Given that \(\frac{x}{y}=\frac{3}{2}\) Now, EF || GH and AB is a transversal. ∴ Its supplement = 180° – x As angles ∠QRS and ∠CSR are alternate interior angles and are equal. Let each angle be x. Tags: Question 15 . and its supplement = 180° – x= 180°- 100 = 80° (b) 144° 2x = 120° ⇒ y = 180° – 30° = 50° (c) 110° Also, BC || DT and DC is a transversal. ∴ ∠1 = 30° ——– (i) [Corresponding angles] Solution: ⇒ 42° + ∠QUR = 180° [Using (i)] Question 82. As ∠APS and ∠PSC are interior angles on the same side of transversal EF and are supplementary. Q. Angles which are both supplementary and vertically opposite are An angle that is greater than 180 degrees is called a reflex angle. (d) 60° 2. always. 6. (iii) There is no pair of vertically opposite angles and no angles are in the form of linear pair. (a) Since, PQ || SR and RP is a transversal False. \(\Rightarrow x=\frac{180^{\circ}}{5}=36^{\circ}\) ∴ Its supplement = 180° – x Solution: True or False: The Vertical Angle Theorem states that if two angles are vertical angles, then they have equal measure. Question 26. Now, ∠BOC = (x + 5)° = (35 + 5) = 40° (c) write all the pairs of vertically opposite angles. (c) (108 – b)° Question 45. In a pair of complementary angles, each angle cannot be more than _________ ∴ ∠ABC + ∠BCD = 180° [Co-interior angles] The diagonals of a quadrilateral_____bisect each other. (d) 120° ∴ 4c = 120°      [Corresponding angles] False \(\Rightarrow \quad a=\frac{180}{5}=36\) Question 83. (b) 45° Solution: ∴ ∠x = 35° [Alternate interior angles] ∠1 and ∠2; ∠1 and ∠4; ∠2 and ∠3; ∠3 and ∠4 are four pairs of adjacent angles. (b) 67° 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. In the given figure, PA || BC || DT and AB || DC. Three lines AB, CD and EF intersect each other at O. ⇒ ∠APR = 130° Now, CD and EF intersect each other at O. Question 59. Two angles making a linear pair are always adjacent angles. (c) 20°, 50° Which of the following statements is NOT correct? Also, p || q and l is a transversal. (vii) The diagonals of a trapezium, divide each other into proportional segments. Thus, x = 114° and y = 132°, Question 108. (c) 145° 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. ⇒ ∠2 = 30° ———– (ii) (a) Both statements p and q are true. 45° : Given, angle = 45° Answer. Then, which one of the following is not true? Consecutive interior angles. Two vertically opposite angles are always equal. always. Are Vertical Angles Adjacent? Thus, ∠EFD = 70°, Question 93. ⇒ 5b – 180° – 80° = 100° These are corresponding angles, therefore they are equal. (c) 70°, 110° Now, 2a + b = 2 × 132° + 132° Angles may be classified based on their angle magnitude. Find x. (d) 64° Thus, a = 67° and b = 48°, Question 102. Solution: ⇒ ∠COA = 90° – 49° [∵ ∠BOC = 49° (given)] In the given figure, l || m || n. ∠OPS = 35° and ∠QRT = 55°. 300 seconds . ... Property: If two lines intersect each other, then the vertically opposite angles are equal. = 90°. (d) 60° Question 61. alternate interior angles have one common _________ False True: (i) vertex is always common, ⇒ 5y = 180° – 30° = 150° ∴ ∠AOD = 139°, Question 94. Vertical Angles: Theorem and Proof. Find the value of a + b. The supplement of the right angle is always _________ angle. true. There are three types of angles formed by parallel lines and a transversal. In figure, OB is perpendicular to OA and ∠BOC = 49°. Question 112. Now, p || q and m is a transversal. Thus, d = 142° ⇒ ∠Q = 180° – 60° = 120°, Question 13. ∴ Let a = 3x and b – 2x Also, AB || DF and BD is a transversal. (c) PQ || RS, line l is a transversal. Find the measure of the segment. The greater the angle, the better chance the player has of scoring a goal. An angle formed by rays AB and BC at vertex B is denoted by ∠ABC. Solution: (c) 20° Now we read the value on the inner scale for the position of line BA. The common point is called its vertex of the angle. ∴ ∠c + ∠2 = 180° [Linear pair] Question 89. ⇒ ∠BOC + ∠COA = 90° According to question, As ∠EPQ and ∠GQP are interior angles on the same side of transversal AB and are supplementary True False: Q 2: Any two right angles are supplementary. (b) complementary An angle is more than 45°. ⇒ 50° + ∠BCD = 180° true or false 1.vertically opposite angles are always supplementary. ∴ 90°- x = 79° If ∠AOE = 30° and ∠DOB = 40° (see figure), find ∠COF. (b) If one of the angles is obtuse, then other angle of a linear pair is acute. We have, Pair of opposite Angles add up to 360° Answer the questions below. (b) complementary angles. ⇒∠APQ + ∠QPR = 130° ⇒ x = 28° As two right angles are supplementary to each other. (a) 95°, 85° According to question, Sometimes. (c) ∠6 = ∠7 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. ⇒ ∠2 = 180° – (2a+ b)° ——– (ii) [∵ ∠1 = (2a + b)° (given)] NCERT Exemplar Class 7 Maths Chapter 5 Lines and Angles are part of NCERT Exemplar Class 7 Maths. Given two parallel lines are cut by a transversal, their same side exterior angles are congruent. An angle measures the amount of turn. A straight angle is an internal angle which is equal to 180°. (iv) Let the angle between c and fig ∠4. One complete rotation of minute hand in one hour makes angle of ……. An angle which is half of its supplement is of ∴ Parallel, Question 50. Vertically opposite angles are always ⇒ (3a – b)° = 180° – (2a + b)° NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12. ⇒ 4x = 180° Solution: a and b are on the opposite side of transversal l. (i) ∠AOB and ∠BOC; ∠AOC and ∠COD; ∠AOB and ∠BOD; and ∠BOC and ∠COD are adjacent angles. ∠APS + ∠PSC = 130° + 50° = 180° [∵ ∠P and ∠Q are supplementary angles] Line BC has been extended as line CD. On a picture below angles #/_KML# and #/_KMH# are supplemental since together they form a straight angle #/_LMH#.. In the given figure, AB||CD. Look at the figure above. (d) ∠2 + ∠3 = 180° In a parallelogram, the opposite angles are equal. (ii) ∠x and ∠y are complementary angles. The two angles are supplementary angles. (d) 144° These angles are on the same side of transversal CD. Solution: Solution: This gives a measure of the angle. ∴ ∠1 = ∠2 [Alternate interior angles] Two angles that have a common vertex and opposite to each other formed by the same two lines are called vertically opposite angles. Since, PQ || RS and TR is a transversal. Solution: 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. ⇒ ∠1 = 70° [Using (ii)] What is the type of other angle of a linear pair if True. Which of the following is false? ⇒ 5a = 180° – 130° = 50° Since, AF || ED and FD is a transversal. ∴ ∠TUR = ∠UVQ = 122° [Corresponding angles] Measures (in degrees) of two supplementary angles are consecutive odd integers. As if both adjacent angles are acute angles, then they do not form a linear pair. Find the values of a, b and c. (c) ∠3 + ∠8 = 180° The Exterior Angle is the angle formed outside a geometric shape between a side of a shape and the extended line of another side. A point has no shape. Solution: True or False. (a) 20°, 50° Question 7. Solution: Vertical Angles are a pair of nonadjacent anglesopposite each other formed when two lines cross.Vertical angles are two angles opposite of each other. ∴ EF and GH are not parallel lines. Solution: (c) a is false and b is true (c) 5° ⇒ (x – 10)° +(4x – 25)° + (x + 5)° = 180° [Angles on a straight line] (c) (i) is false but (ii) and (iii) are true Thus, the greater angle is 100°. (a) 150° False (a) 29° The two vertically opposite angles are equal. ∴ ∠ABP = ∠CBQ ——– (1) The angle The angles x and 90° – x are An angle is a figure formed by two rays meeting at a common point. ∴ b + 132° = 180° [Co-interior angles] (iii) ∠TSV and ∠USV; ∠SVT and ∠SVU are adjacent angles. ∴ These angles are complementary. ∴ ∠2 + ∠5 = 180° —— (i) [Co-interior angles] Understanding Trigonometric Ratios With Application to Triangles – Maths Tips. C. This statement is true because a triangle cannot have two or more angles that are greater than 60°. The two complementary angles not necessarily need to be adjacent angles. An obtuse angle is more than 90 but less than 180 degrees. In Parts (a) and (b) given below, it may help to trace the diagrams and draw and measure angles. ⇒ 3a – b + 2a + b = 180 ⇒ 5a = 180 Question 74. If an angle is 60° less than two times of its supplement, then the greater angle is Distinct. Solution: a = d true. A linear pair may have two acute angles. 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The measurement of a straight angle is. (d) ∠3 = ∠7 ∴ ∠COF = ∠EOD = 110° [Using (i)] [Vertically opposite angles] \(\Rightarrow y=\frac{150^{\circ}}{5}=30^{\circ}\) q: a and b are forming a pair of adjacent angles. (d) equal Help Amisha in finding the angles. ⇒ ∠2 = ∠y = 120° [Vertically opposite angles] ∠FOR + ∠QRH = 123° + 57° = 180° In one particular case, when vertical angles are right … 27. Arm, Question 47. In the given figure, AE || GF || BD, AB||CG|| DF and ∠CHE = 120°. ∴ ∠1 = ∠3 [Corresponding angles] As one acute angle and one obtuse angle can make two supplementary angles. In the given figure, line l intersects two parallel lines PQ and RS. Question 42. In each of the following figures, write, if any, ⇒ x = 90° – 79° ⇒ x – 11° Q. Question 3: Look at the figure below. ⇒ x + 4x = 720° Given that. Let x = 3k and y – 2k Solution: Write down each pair of adjacent angles shown in the following figures: Also, m || n and QR is a transversal. ∴ ∠1 + ∠x = 180° [Co-interior angles] False ∴ x = 85° [Altemate interior angles] (a) 10° We have, Name the pairs of supplementary angles in the following figures: ⇒ ∠ABP + 46° + ∠ABP = 180° [Using (1) (ii). Solution: TRUE or FALSE: The sides of one of two vertical angles are opposite rays to the sides of the other ... About this tutor › true because opposite rays lie on the same line and intersect in only one point. ∴ ∠b + ∠1 = 180° [Linear pair] Solution: The red angles ∠ JQM and ∠ LQK are equal, as are the blue angles ∠ JQL and ∠ MQK. Solution: ⇒ 2x = 166° \(\Rightarrow x=\frac{120^{\circ}}{2}=60^{\circ}\) Also, TR || QU and RS is a transversal. Thus, the required angles are 60° and 30°. (c) both are acute Since, vertically opposite angles are equal. ⇒ 3x = 180° – x ⇒ 3x + x = 180° \(\Rightarrow b=\frac{100^{\circ}}{5}=20^{\circ}\). Question 28. ∴ ∠QOR = 3y = 3× 30° = 90°, Question 15. True Question 5. 1. ∴ ∠POR + ∠ROQ = 180° [Linear pair] ∴ a = 36 This contradicts Proposition 16 which states that an exterior angle of a triangle is always greater than the opposite interior angles. State with reasons whether the following statements are ‘true’ or ‘false’. ∴ 2x = 2 × 22° = 44° and 2x + 2 = 44° +2 = 46° (i) Name all the pairs of adjacent angles. Solution: ⇒ ∠QUR = 180° – 42° = 138°. (b) supplementary 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°. Solution: Solution: Solution: (a) (2 + b)° The following angles are also supplementary as the sum of their measures is equal 180 degrees. When the sum of the measures of two angles is 90°, the angles are called (а) supplementary angles (b) complementary angles (c) adjacent angles (d) vertically opposite angles. (iii) No, a and b are not adjacent angles as they don’t have common vertex. (b) 4th player has the greatest kicking angle. c || f and a is transversal. Two adjacent angles always form a linear pair. ∴ Its supplement = 180° – x 100° + y = 180 ⇒ y = 180° – 100° = 80° (c) 55° (d) 62° Justify your answer. From (i), (c) 64° (a) If one of the angles is acute, then other angle of a linear pair is obtuse. ⇒ f = 108°, Question 37. 5.if a transversal intersects two lines and the corresponding angles are equal,then the two lines are parallel. and 2x + 3 = 2 × 44° + 3 = 88° + 3 = 91° Solution: Two lines ABand CD intersect each other at point O, then, there are two pairs of vertically opposite angles. True, Question 62. Two lines will meet in one point only when they are parallel. Its complement -90° – x Definition and properties of vertical (or opposite) angles. In the given figure, the value of a is If ∠ABC = 46°, then ∠ABP is equal to (d) 22.5° ⇒ (3a + 5)° + (2a-25)° = 180° Question 30. Question 4. Question 104. (a) 60°, 30° ⇒ x+y – 90° ——- (i) 7. 2x + 2x + 2 = 90° An angle is generally named by three consecutive alphabets such as A, B and C or X, Y and Z. ∠ACD +∠DCB = 90° ∴ ∠POR + ∠ROT + ∠TOQ = 180° ... Find the angles. a = d true. Thus an angle has three parts one vertex and two sides. This goes on increasing with time. As one angle is 45°, the other angle = 90-45= 45°, 2. (a) supplementary (b) equal (c) unequal (d) none of these. Then, Thus, one angle is 89° and other is 91°, Question 99. \(\Rightarrow x=\frac{166^{\circ}}{2}=83^{\circ}\) You will understand this more clearly with the help of the figure given below: The opposite angles of a parallelogram are supplementary. (c) 80 Vertical angles are also called opposite angles. Angles opposite to equal sides of an isosceles triangle are equal. Solution: (b) When a transversal cuts two parallel lines, each pair of alternate interior angles are equal. 45 to 48). Directions: In questions 42 to 56, fill in the blanks to make the statements true. a: If two lines intersect, then the vertically opposite angles are equal. Note: A vertical angle and its adjacent angle is supplementary to each other. If ∠α =30°, find value of ∠β. ∴ y + 80° = 180° [Co-interior angles] Since, QP || RS and QR is a transversal. (a) When a transversal cuts two parallel lines, each pair of corresponding angles are equal. Question 24. Thus, both the angles are of 83°. (c) ∠a + ∠d = 180° Such angles are also known as supplementary angles. (a) 40° In the given figure, a and bare ∴ AB || CD. Answer: (b) complementary angles Hint: Definition of complementary angles (a) Botha and bare true Measures (in degrees) of two complementary angles are two consecutive even integers. Symbol for an angle is ∠. (d) 90° (c) (45°, 45°) and (60°, 30°) are the two pairs of angles formed by different positions of two players such that they are complement to each other. As ∠β =120°, ∠ α = 180-120 = 60°. but ∠a ≠ ∠d, Question 12. Find the value of the complementary angle of an angle measuring 30°. (d) 105°, 75° (d) 135° (ii) Every rhombus is a rectangle. In the given figure, QP || RS. \(\Rightarrow x=\frac{180^{\circ}}{3}=60^{\circ}\) \(\Rightarrow \quad a=\frac{120^{\circ}}{6}=20^{\circ}\) ... the bisectors of vertical angles are opposite rays. Two supplementary angles are always obtuse angles. sum of interior angles on the same side of a transversal is _________ True, as all the angles are right angles and the diagonals are congruent to each other. Answer: (b) equal. (a) vertically opposite angles ∴ b = 55° [Alternate interior angles] 1. Step-by-step explanation: Yes, they do give vertical angles, which by definition means opposite angles created by intersecting lines. Solution: \(\Rightarrow \quad y=\frac{180^{\circ}}{9}=20^{\circ}\), Question 17. As ∠RSP and ∠QPD are corresponding angles and are not equal. (False) (vi) 30° is one-half of its complement. ∠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. As if both angles are 89° and 89°, even then they cannot make the sum 180°. (a) Seven football players are practicing their kicks. Solution: We have, Then, According to question, Solution: (ii) one arm is always common, and (a) supplementary Solution: These angles are always equal to each other. (d) Let the angle be x. Find each of the angles. ⇒ B = 90° – A (a) ∠TOS and ∠SQR is a pair of complementary angles. True or false. \(\Rightarrow x=\frac{720^{\circ}}{5}=144^{\circ}\), Question 16. (a) interior angles on the same side of the transversal Which player has the best the greatest) kicking angle? 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… In the given figure, ∠AOC and ∠BOC form a pair of (b) 24° The angle which makes a linear pair with an angle of 61° is of It is denoted by ∠θ. (c) Since, PQ || RS and line 1 is a transversal. Its complementary angle must be less than 45°. ∴ ∠POQ + ∠QOR = 180° [Linear pair] In Geometry we will learn more about the angles with magnitudes between 0 and 360°. (iv) ∠AOC and ∠AOD; ∠BOC and ∠BOD; ∠AOC and ∠BOC, ∠AOD and ∠BOD are adjacent angles. ... State whether the given statements are true or false: Question 1. Question 57. Answer: a = 140° , b = 40° and c = 140° . Geometry Finals Semester 1 Always, Sometimes, Nevers. (d) Since, sum of the angles about a point is 360° Vertical Angles Theorem states that vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent. ∴ a + b = c [Alternate interior angles] In the given figure, a = 40°. In the given figure, POQ is a line, then a is equal to Question 86. Question 79. (ii) ∠PQT and ∠PQR; ∠ORU and ∠QRP; ∠RPS and ∠RPQ are adjacent angles. (a) one of its angles is acute? The following angles are also complementary as the sum of their measures is equal 90 degrees, Two angles whose measures add to 180 degrees are called Supplementary Angles. Solution: ⇒ ∠POR + ∠QOS = 180° – 90° = 90° ——- (i) (c) When a transversal cuts two parallel lines, each pair of interior angles on the same side of the transversal are supplementary. (c) m and n are two straight lines and I is a transversal intersecting both lines m and n. (ii) AB and CD ∵ AB is a straight line. Solution: ∴ b + d = 180° [Co-interior angles] b: If a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is 180°. (c) alternate interior angles Question 75. Solution: 2. true or false: planes are created by 3 collinear points. ∴ ∠TRU + ∠QUR = 180° [Co-interior angles] The value of a is Solution: Vertically Opposite Angles. Since, 90° + 90° = 180°, a supplementary angle. ∴ (a + b) + 65° = 180° [Co-interior angles] Now, PQ || RT and RQ is a transversal. On a picture below angles #/_A# are vertical, as well as angles #/_B#.. Solution: Find ∠PQR. Now, l || m and p is a transversal. Both angles of a pair of supplementary angles can never be acute angles. ∴ ∠APR = ∠PRD [Alternate interior angles] How many degrees are in a “straight angle”? (d) (ii) is false ⇒ ∠b = 180° – 30° = 150° [Using (1)] ∴ ∠QOS = 5 ∠POR = 5 × 15° = 75°, Question 23. Question 111. (b): Since, vertically opposite angles are equal. (d) both p and q are false Opposite, Question 49. Solution: It is a right angle and measures 90°, Question 2: Look at the figure below and find ∠ACD, ∠ACB is a right angle Now, c || d and e is a transversal. in a plane, the relation "is perpendicular to" is transitive. Solution: The angle formed at the vertex B by the two rays AB and BC is called ∠ABC. (a) 120° (d) both a and b are false ∴ a = 132 [Corresponding angles] In the given figure, AB || CD, AF || ED, ∠AFC = 68°and ∠FED = 42°. Two angles are vertical. ∠POR and ∠ROQ; ∠ROQ and ∠OOS; ∠QOS and ∠SOP; ∠SOP and ∠POR; ∠ROT and ∠TOS; ∠OOT and ∠POT are linear pairs. (a) 90° Answer: True 2.Two lines in a plane always intersect in a point. (iii) ∠1 and ∠2, ∠3 and ∠4, ∠5 and ∠6 are three pairs of supplementary angles. ⇒ 60° + 20 = 180° ∴∠CHE = ∠HCB – 120° ———- (i) [Alternate interior angles] Solution: For given figure, statements p and q are given below: ANSWERS. If the angles are adjacent to each other after the intersection of the lines, then the angles are said to be adjacent. (c) making a linear pair Let A and B are two angles making a complementary angle pair and A is greater than 45° Thus, ∠COF = 110°, Question 95. (c) 13° Solution: ⇒ ∠c + 30° = 180° [Using (iii)] ⇒ x = 360°- 210° (i) EF and GH Now, SOT is a straight line (d) 20° This is enshrined in mathematics in the Vertical Angles Theorem. Solution: (i) False (ii) True (iii) True (iv) False (v) True (vi) True (vii) True 12. Solution: ⇒ a = 180° – 65° = 48° [Using (i)] (d) 120° ⇒ 3x = 300° (b) Let the angle be x. ⇒ 4x = 90° – 2 = 88° ∠d = ∠c [Vertically opposite angles] Vertically opposite angles form a linear pair. The sum of the Interior Angle and the Exterior Angle are 180°. The legs of a stool make an angle of 35″ with the floor as shown in figure. An Interior Angle is an angle inside the shape ABC. Since, AE || BD and CH is a transversal. Solution: (c) 122° (b) Since, POQ is a straight line If angle with measure x and y form a complementary ... answer as true or false. Maths Help, Free Tutorials And Useful Mathematics Resources. (b) We know that angle of incident and angle of reflection is same. ⇒ 5b + 2 × 40° = 180° False ⇒ 9y = 180° Solution: ⇒2x = 180° – x False True: Q 4: Any two supplementary angles are adjacent. 2x = 180° + 20° = 200° (a) Since, POR is a straight line. ⇒ x = 180° – 61° = 119° Two right angles are complementary to each other. (a) ∠1 + ∠5 = 180° (b) one of its angles is obtuse? Solution: Solution: ⇒ (6x – 30) = 180 ⇒ 6x – 180 + 30 = 210 3. x + 61° = 180° [Linear pair] \(\Rightarrow a=\frac{200^{\circ}}{5}=40^{\circ}\), Question 14. In the given figure, show that Sum of the measure of an angle and its vertically opposite angle is always. In the given figure, POQ is a line. If the complement of an angle is 799, then the angle will be of 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 . 60° + y = 90° \(x=\frac{1}{3}\left(180^{\circ}-x\right)\) Solution: What is value of the supplementary angle of an angle measuring 75°? 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. Solution: In the given figure, examine whether the following pairs of lines are parallel or not: A pair of vertically opposite angles are always equal to each other. Solution: (b) 50°, 20° (i) ∠1 and ∠3; ∠2 and ∠4; ∠5 and ∠7; ∠6 and ∠8 are four pairs of vertically opposite angles. ∴ x + y = 85° + 50° = 135°, Question 41. (c) 136° ∴ 2x + 1 = 2 × 44° + 1 = 88° + 1 = 890 Now, 40° + 90° + 5a = 180° [Angles on a straight line BOE] The adjacent angles are the angles that have a common vertex. Called complementary angles not necessarily be adjacent angles 34° [ Alternate interior angles ],... Angles need not necessarily need to be supplementary, if two lines each. Questions below chance of scoring a goal 30° [ vertically opposite angles this be. But from right to left below: a line angles have a common ray one acute angle can have angles! When they are congruent ∠TOR ; ∠SQR and ∠PQS are two angles that are opposite each formed! Vertical '' angles figure ), show angles formed by rotating a single ray about its vertex the... These lines at p and 4 only if both adjacent angles are in vertically opposite angles are always equal true or false,...: p: a = 180° – 100° = 80° + 55° = 100°, Question.!, you already know the answer the maximum angle trace the diagrams and draw and measure angles CH. 130° = b thus, when vertical angles, then value of x.... Of intersecting lines Question, you already know the answer || CD AF. Parallelogram, the better chance of scoring a goal from position a than from position a than from a! X = 85° [ Altemate interior angles ] ⇒ 100° + a = 45° + 55° =,! ( ∵ 45° + 45° = 90° ∠ACD +30° = 90° Hence ∠ACD = 60° one vertex one. Two arms two and is a transversal, two pair of adjacent angles are.! The values of a and bare forming a pair of Alternate interior angles are right and! Pq || RT and PR is a transversal intersect two lines, and the other of... 30° as shown in fig. ( i ) angles forming a pair of angles! And East are making a linear pair is acute, 7, 8 9... Incident ray and BC is the type of other angle of one is correct angle f is vertically angles... Ut are parallel f = 108°, Question 106 angles ( b ) one the... ∠Pqt and ∠PQR ; ∠ORU and ∠QRP ; ∠RPS and ∠RPQ are adjacent angles are always the side!, Nevers were supplementary, as all the pairs of opposite angles always complete eachother of one congruent! 30° and ∠DOB = 40° and c is a transversal PR is a figure formed two! And ∠QRP ; ∠RPS and ∠RPQ are adjacent angles are equal ∠x and ∠y complementary! = 110° [ Alternate interior angles ] Now, e || f and c or x, y Z! Their kicks figures ) are the following pairs of supplementary angles therefore, angles given in option ( b 4. Ac, and the lines p and Q is a transversal with two distinct parallel lines PQ and RS greater! Angles opposite of each other at right angles are always supplementary an acute is always equal ( ) 310 2... ) 30° is one-half of its angles is right ∠BOC and ∠BOD ; ∠AOC and,. Called triangle ( we will learn more about triangle in other article.... Given figures ) are the two hands POR is a transversal statement is true or False: Question.! The help of a pair of complementary angles Hint: definition of complementary angles )..., their same side of a stool make an angle is an angle is degree 34° Alternate! ∠Aod ; ∠BOC and ∠BOD are adjacent angles on the same thing degrees from 0 180! And Useful mathematics Resources intersects these lines at _________ points equal to other... Either both acute angles, two angles are two pairs of complementary angles 3, and 4.... ∠Rpq are adjacent angles are always supplementary to each other, form a linear pair ] ⇒ f =,... ∠Tqs and SQR ; ∠PQT and ∠PQR ; ∠ORU and ∠QRP ; ∠RPS and ∠RPQ are adjacent.! Angle of an angle that is greater than or equal to 180 from left to right their arms opposite...

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