Mathematics
In the given figure, O is the centre of the circle. If ∠CBD = 25° and ∠APB = 120°, find ∠ADB.
Circles
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Answer
From figure,
⇒ ∠CPB + ∠APB = 180° [Linear pair]
⇒ ∠CPB = 180° - ∠APB
⇒ ∠CPB = (180° − 120°) = 60°.
By angle sum property of a triangle we get,
⇒ ∠PCB + ∠CPB + ∠PBC = 180°
⇒ ∠PCB + 60° + 25° = 180°
⇒ ∠PCB + 85° = 180°
⇒ ∠PCB = 180° - 85°
⇒ ∠PCB = 95°
⇒ ∠ADB = ∠ACB = 95° [Angles in same segment of a circle are equal]
Hence, the value of ∠ADB = 95°.
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