Question

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

पर्याय

• 130°

•  115°

• 65°

• 165°

Answer 1

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,  `angleAPC = (angleAOC)/2 = 130/2 = 65°`

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

Therefore,

\[\angle ABC + \angle APC = 180°\]
\[ \Rightarrow \angle ABC + 65° = 180° \]
\[ \Rightarrow \angle ABC = 180° - 65° \]
\[ \Rightarrow \angle ABC = 115°\]