Practice with Central & Inscribed Angles - MathBitsNotebook(Geo) - Free Printable

Let’s solve this step by step.

We are given a circle with center O. Points A, B, and C are on the circle. Angle ABC is 62°, and we need to find angle AOC, which is labeled as x.

First, remember this key rule in circles:

> The angle at the center of a circle (angle AOC) is twice the angle at the circumference (angle ABC) when both angles stand on the same arc — in this case, arc AC.

So, if angle ABC = 62°, then angle AOC = 2 × 62°.

Let’s calculate that:

2 × 62 = 124

So, x = 124°

Double-check: Yes, this is a standard circle theorem — central angle is double the inscribed angle subtended by the same arc. No tricks here.

Final Answer:
124