Question:
In the given figure, ‘O’ is the centre of the semi-circle and ∠MON =48°, Find ∠MRP.
In the given figure, ‘O’ is the centre of the semi-circle and ∠MON =48°, Find ∠MRP.
Updated On: Sep 13, 2024
- 60°
- 66°
- 54°
- 72°
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The Correct Option is B
Solution and Explanation
The correct option is (B): 66°
Clearly, ∠PMQ is a semi-circular angle.
So, ∠PMQ = 90°
Again, ∠MPN = (\(\frac{1}{2}\)) × ∠MON = (\(\frac{1}{2}\)) × 48 = 24° {The angle subtended
by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle}
In ΔMPR,
∠MRP = 180° – 90° – 24° = 66°
Clearly, ∠PMQ is a semi-circular angle.
So, ∠PMQ = 90°
Again, ∠MPN = (\(\frac{1}{2}\)) × ∠MON = (\(\frac{1}{2}\)) × 48 = 24° {The angle subtended
by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle}
In ΔMPR,
∠MRP = 180° – 90° – 24° = 66°
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