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Question
In the given figure, AB is the diameter of the circle with centre O.
If ∠ADC = 32°, find angle BOC.
Solution
Arc AC subtends ∠AOC at the centre and ∠ADC at the remaining part of the circle
∴ ∠AOC = 2∠ADC
`=>` ∠AOC = 2 × 32° = 64°
Since ∠AOC and ∠BOC are linear pair, we have
∠AOC + ∠BOC = 180°
`=>` 64° + ∠BOC = 180°
`=>` ∠BOC = 180°
`=>` ∠BOC = 180° – 64°
`=>` ∠BOC = 116°
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