Question

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

Options

• 150°

• 75°

• 45°

• 60°

Answer 1

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

Explanation:

Since ∠POR and ∠QOS are in the ratio 1:5. Let angles will be x and 5x, respectively. We know that, the sum of angles forming linear pairs is 180°.

∴ ∠POR + ∠ROS + ∠QOS = 180°

⇒ x + 90° + 5x = 180°

⇒ 6x = 180° – 90°

⇒ 6x = 90°

⇒ x = `90^circ/6`

⇒ x = 15°

∴ ∠QOS = 5x = 5 × 15°

⇒ ∠QOS = 75°