Question

In the given figure, O is the centre of the circle. $\angle \text{PBC}={25}^{\circ }\text{and}\angle \text{APB}={110}^{\circ }$, find the value of $\angle \text{ADB.}$

Answer 1

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 °