In Fig. 5.19, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1 : 5. Then, ∠ QOS measures
a. 150°
b. 75°
c. 45°
d. 60°

Solution:

Given, ∠ROS is a right angle

∠POR and ∠QOS are in the ratio 1 : 5.

We need to find the measure of ∠QOS.

Let ∠POR be x

Since the ratio is 1 : 5, then ∠QOS be 5x

We know that the linear pair of angles is always equal to 180 degrees.

So, ∠POR + ∠ROS + ∠QOS = 180°

x + 90° + 5x = 180°

6x = 180° - 90°

6x = 90°

x = 90°/6

x = 15°

5x = 5(15°)

x = 75°

Therefore, ∠ QOS = 75°

✦ Try This: From the given figure, find the measure of ∠BOC.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5

NCERT Exemplar Class 7 Maths Chapter 5 Problem 22

In Fig. 5.19, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1 : 5. Then, ∠ QOS measures: a. 150°, b. 75°, c. 45°, d. 60°

Summary:

∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1 : 5. Then, ∠ QOS measures 75°.

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