Question

1. Suppose that angle AOC, a central angle of a circle, and angle ABC, an inscribed angle of the same circle, intercept the same arc. Circle the correct word(s) in the sentence. The measure of angle AOC is [half | equal to | double] the measure of angle ABC.​

Answer 1

The measure of angle AOC is double the measure of angle ABC.

Explanation:

You want to know the relationship between central angle AOC in circle O and inscribed angle ABC subtending the same arc AC.

Inscribed angle

The measure of an inscribed angle is half the measure of the arc it intercepts. The measure of a central angle is exactly equal to the measure of the arc it intercepts. (That's how the arc measure is determined.)

Hence, the measure of angle AOC is double the measure of angle ABC.

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Additional comment

Inscribed : central = 1 : 2

Central : inscribed = 2 : 1

You need to be a little careful of the wording of the relationship. Which is double and which is half can be confused when it's written in words. On a diagram, the angle with its vertex in the center will obviously be larger than the one with its vertex on the circle.