Mathematics
In the given figure, AB is the diameter of the circle with centre O.
If ∠ADC = 32°, find angle BOC.
Circles
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Answer
We know that,
Angle at the centre is twice the angle at remaining circumference.
Arc AC subtends ∠AOC at the centre and ∠ADC at the remaining part of the circle.
⇒ ∠AOC = 2∠ADC
⇒ ∠AOC = 2 x 32° = 64°
From figure,
∠AOC and ∠BOC are linear pair,
∴ ∠AOC + ∠BOC = 180°
⇒ 64° + ∠BOC = 180°
⇒ ∠BOC = 180° - 64° = 116°.
Hence, ∠BOC = 116°.
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