# AOCB is a quadrilateral in circle with centre O, angle AOC = 130 degrees. Find angle CBA.

A quadrilateral can be defined as a closed, two-dimensional shape which has four straight sides, angles, edges and vertices

A circle can be defined as a closed, two-dimensional curved shape with no corners or edges

## Answer: For a quadrilateral AOCB in a circle with centre O and angle AOC = 130 degrees, value of angle CBA is 115 degrees

We will be using the properties of chord of a circle and cyclic quadrilateral to calculate the value of angle CBA

**Explanation:**

Let's take a point 'P' on the circumference and join AP and CP as shown below

We know that,

**The angle subtented by the chord at the centre is twice of the angle subtended by the same chord on any part of the circumference**

Thus, ∠APC = ∠AOC/2 = 130°/2 = 65°

We know that,

ABCP is a cyclic quadrilateral

Hence, ∠APC + ∠CBA = 180° (Since, sum oppposite angles of a cyclic quadrilateral is supplementary)

=> ∠CBA = 180° - 65° (Since, ∠APC = 65° )

=> ∠CBA = 115°