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Question
In the following figure, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1 : 5. Then, ∠QOS measures ______.
Options
150°
75°
45°
60°
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Solution
In the following 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 pair 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°
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