Mathematics
In the given figure, O is the centre of the circle and ∠BDC = 36°. The measure of ∠ACB is :
36°
54°
72°
46°
Circles
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Answer
We know that,
The angle which an arc subtends at the center is double that which it subtends at any point on the remaining part of the circumference.
∴ ∠BOC = 2∠BDC
∠BOC = 2(36°) = 72°
∠AOB + ∠BOC = 180°
∠AOB = 180° - ∠BOC
∠AOB = 180°- 72° = 108°
∴ ∠ACB = ∠AOB
∠ACB = = 54°.
Hence, option 2 is the correct option.
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