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In a pair of adjacent angles, (i) vertex is always common, (ii) one arm is always common, and (iii) uncommon arms are always opposite rays.Then (a) All (i), (ii) and (iii) are true (b) (iii) is false (c) (i) is false but (ii) and (iii) are true (d) (ii) is false

The correct answer is (b) (iii) is false Solution Two angles are called adjacent angles if they have a common vertex and a common arm but no... View Article

. In which of the following figures, a and b are forming a pair of adjacent angles?

The correct answer is (d) a and b are forming a pair of adjacent angles. Solution The two angles are said to be adjacent angles when they... View Article

In figure if QP || SR, the value of a is (a) 40⁰ (b) 30⁰ (c) 90⁰ (d) 80⁰

The correct answer is (c) 90o Solution To determine the value of ‘a’, draw a line XY, to cut at ‘a’. So, XY... View Article

In figure the value of a is (a) 20⁰ (b) 15⁰ (c) 5⁰ (d) 10⁰

The correct answer is (d) 10o Solution ∠AOF = ∠COD = 90o [because vertically opposite angles] We observe that sum of... View Article

In figure ∠AOC and ∠ BOC form a pair of (a) vertically opposite angles (b) complementary angles (c) alternate interior angles (d) supplementary angles

The correct answer is (d) supplementary angles Solution When the sum of two angles is 180°, then the angles are known as supplementary... View Article

For figure statements p and q are given below p : a and b are forming a linear pair. q : a and b are forming a pair of adjacent angles. Then, (a) both p and q are true (b) p is true and q is false (c) p is false and q is true (d) both p and q are false

The correct answer is (a) both p and q are true Solution p : a and b are forming a linear pair. q : a and b are forming a pair of adjacent angles.... View Article

Statements a and b are as given below: a : If two lines intersect, then the vertically opposite angles are equal. b : If a transversal intersects, two other lines, then the sum of two interior angles on the same side of the transversal is 180⁰. Then (a) Both a and b are true (b) a is true and b is false (c) a is false and b is true (d) both a and b are false

The correct answer is (b) a is true and b is false Solution a: If two lines intersect, then the vertically opposite angles are equal. b: If a... View Article

In figure ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1: 5. Then, ∠QOS measures (a) 150 (⁰b) 75⁰ (c) 45⁰ (d) 60⁰

The correct answer is (b) 75o Solution When the sum of two angles is 180°, then the angles are known as supplementary angles. In other... View Article

If two supplementary angles are in the ratio 1: 2, then the bigger angle is (a) 120⁰ (b) 125⁰ (c) 110⁰ (d) 90⁰

The correct answer is (a) 120o Solution We know that when the sum of two angles is 180°, then the angles are known as supplementary... View Article

In figure, a and b are (a) alternate exterior angles (b) corresponding angles (c) alternate interior angles (d) vertically opposite angles

The correct answer is (c) alternate interior angles Solution The angles which are formed inside the two parallel lines, when intersected by a... View Article

In figure PQ || SR and SP || RQ. Then, angles a and b are respectively (a) 20⁰, 50⁰ (b) 50⁰, 20⁰ (c) 30⁰, 50⁰ (d) 45⁰, 35⁰

The correct answer is (a) 20o, 50o Solution From the figure, we observe that ∠QRP = ∠RPS = 50o … [because interior alternate... View Article

The difference of two complementary angles is 30⁰. Then, the angles are (a) 60⁰, 30⁰ (b) 70⁰, 40⁰ (c) 20⁰, 50⁰ (d) 105⁰, 75⁰

The correct answer is (a) 60o, 30o Solution When the sum of the measures of two angles is 90o, then the angles are called complementary angles.... View Article

In figure, PA || BC || DT and AB || DC. Then, the values of a and b are respectively (a) 60⁰, 120⁰ (b) 50⁰,130⁰ (c) 70⁰,110⁰ (d) 80⁰,100⁰

The correct answer is (b) 50o,130o Solution We know that, ∠PAB = ∠ABC = 50o … [because interior alternate angles]... View Article

In figure the value of y is (a) 30⁰ (b) 15⁰ (c) 20⁰ (d) 22.5⁰

The correct answer is (c) 20o Solution From the figure, we observe that the Sum of all angles about a straight line given in the figure is equal... View Article

The measure of an angle which is four times its supplement is (a) 36⁰ (b) 144⁰ (c) 16⁰ (d) 64⁰

The correct answer is (b) 144o Solution When the sum of two angles is 180°, then the angles are known as supplementary angles. In other... View Article

In figure POQ is a line. If x = 30°, then ∠ QOR is(a) 90⁰ (b) 30⁰ (c) 150⁰ (d) 60⁰

The correct answer is (a) 90o Solution From the figure we observe that sum of all angles about a straight line given in the figure are equal... View Article

In figure, POR is a line. The value of a is(a) 40⁰ (b) 45⁰ (c) 55⁰ (d) 60⁰

The correct answer is (a) 40o Solution When the sum of two angles is 180°, then the angles are known as supplementary angles. In other... View Article

If angle P and angle Q are supplementary and the measure of angle P is 60⁰, then the measure of angle Q is (a) 120⁰ (b) 60⁰ (c) 30⁰ (d) 20⁰

The correct answer is (a) 120o Solution When the sum of two angles is 180°, then the angles are known as supplementary angles. In other... View Article

In figure lines l and m intersect each other at a point. Which of the following is false? (a) ∠a = ∠b (b) ∠d = ∠c (c) ∠a + ∠d = 180o (d) ∠a = ∠d

The correct answer is (d) ∠a = ∠d Solution From the figure, we observe that ∠a ≠ ∠d ∠a = ∠b [because vertically... View Article

. In figure if AB || CD, ∠ APQ = 50o and ∠PRD = 130⁰, then ∠ QPR is (a) 130⁰(b) 50⁰ (c) 80⁰ (d) 30⁰

The correct answer is (c) 80o Solution From the figure we observe that ∠APR = ∠PRD … [because interior alternate... View Article