What is the measure of angle CBA in quadrilateral AOCB inscribed in a circle with center O if angle AOC is 130 degrees?

In a circle, a key property of angles formed by chords and tangents is that the angle formed at the center of the circle (angle AOC in this case) is twice the angle formed at the circumference (angle CBA) subtended by the same arc.

Given that angle AOC is 130 degrees, we can use this property to find angle CBA:

Step 1: The relationship between the angles is given by:

Angle AOC = 2 × Angle CBA

Step 2: Plugging in the value we have:

130 degrees = 2 × Angle CBA

Step 3: Now, we solve for Angle CBA:

Angle CBA = 130 degrees / 2 = 65 degrees

Conclusion: Therefore, angle CBA measures 65 degrees.