In the given diagram, O is the centre of the circle and ABCD is a cyclic quadrilateral. If ∠CDE = 65°, then the value of x is :

1. 32.5°

2. 65°

3. 115°

4. 130°

In a cyclic quadrilateral,

Exterior angle is equal to the interior opposite angle.

∠CBA = ∠CDE = 65°

We know that,

The angle subtended by an arc at the centre of a circle is twice the angle subtended by it at any point on the remaining part of the circle.

∠AOC = 2 × ∠ABC

x = 2 × 65°

x = 130°.

Hence, option 4 is the correct option.