Question

The measure of ∠ABC is 46°. What is the measure of its intercepted arc AC?

46°
92°
144.44°
23°

Thank you!

Answer 1

The angle ABC is an inscribed angle in a circle.

So, you can use the theorem that says that the measure of an inscribed angle in a circle is half the central angle.

So, the central angle is twice 46°, that is 2 * 46° = 92°.

And you also need to know that the measure of the arc is the same measure of the central angle. So the arc AC measures 92°.

Answer: 92°