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

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

A circle is a closed, two-dimensional curved shape with no corners or edges.

## Answer: The value of angle CBA is 115 degrees.

We will be using the properties of the 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 subtended by the chord at the center is twice 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 the sum of the opposite angles of a cyclic quadrilateral is supplementary)

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

=> ∠CBA = 115°

### Hence, for a quadrilateral AOCB in a circle with center O and angle AOC = 130 degrees, the value of angle CBA is 115 degrees.

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