Question

Angle ABC is inscribed in circle O. Points A, B, and C all lie on the circle, and B is the vertex of angle ABC. Angle ABC measures 47°. What is the measure of angle AOC? Explain your reasoning in complete sentences.

Answer 1

94 degrees

Explanation:

Basically the question is asking to find the angle of the arc AC created by the inscribed angle ABC.

The angle of the arc of an inscribed angle is twice the value of the angle creating it.

Because the distance from the opposite side of the circle is twice longer than coming from the center to create the same arc.

So, an inscribed angle of 47 degrees will create a 94 degrees arc on the circle circumference.