In the given figure, O is the centre of the circle. if ∠PBC = 25° and ∠APB = 110°, find the value of ∠ADB.

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Solution

From the given diagram, we have:

∠ACB = ∠PCB
∠BPC = (180° - 110°) = 70° (Linear pair)

Considering ΔPCB, we have:
∠PCB + ∠BPC + ∠PBC = 180° (Angle sum property)
⇒ ∠PCB + 70° + 25° = 180°
⇒ ∠PCB = (180° – 95°) = 85°
⇒ ∠ACB = ∠PCB = 85°

We know that the angles in the same segment of a circle are equal.
∴ ∠ADB = ∠ACB = 85°

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