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.
visual curriculum