Question

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:

Options

• 32.5°

• 65°

• 115°

• 130°

Answer 1

130°

Explanation:

In a cyclic quadrilateral,

The exterior angle matches the measure of the opposite interior angle. 

Given: ∠CBA = ∠CDE = 65°

We can apply the circle theorem, which states that the angle subtended by an arc at the centre is twice the angle it subtends at the circumference.

∠AOC = 2 × ∠ABC

x = 2 × 65°

x = 130°