Q22 of 113 Page 128

In Fig. 5.19, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1 : 5. Then, ∠QOS measures

Since ∠ROS, ∠POR and ∠QOS forms a linear pair

∠ROS is a right angle

So ∠POR and ∠QOS are complementary angles

Let ∠POR be x, ∠QOS be 5x

x + 5x = 90°

⇒ 6x = 90°

⇒ x = 15°

∠QOS = 15°× 5 = 75°

In Fig. 5.18, a and b are

If two supplementary angles are in the ratio 1 : 2, then the bigger angle is

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 180°.

Then

For Fig. 5.20, 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,