Question

In the given figure, O is the centre of the circle such that ∠AOC = 130°, then ∠ABC =

(a) 130°

(b) 115°

(c) 65°

(d) 165°

Answer 1

(b) 115°

We have the following information in the following figure. Take a point P on the circle in the given figure and join AP and CP.

Since, the angle subtended by a chord at the centre is twice that of subtended atany part of the circle.

So,

Since is a cyclic quadrilateral and we known that opposite angles are supplementary.

Therefore,

$$\begin{gathered} \angle ABC+\angle APC=180° \\ \Rightarrow \angle ABC+65°=180° \\ \Rightarrow \angle ABC=180°-65° \\ \Rightarrow \angle ABC=115° \end{gathered}$$

Hence, the correct answer is optoon (b).