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प्रश्न
In the given figure, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1:5. Then, ∠QOS measures ______.
विकल्प
150°
75°
45°
60°
उत्तर
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°
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