Circle Angles Inside & Out

Front

What is the relationship between the measure of an arc and the angle formed at the center of the circle?

Back

The measure of the angle formed at the center of the circle (∠AOC) is half the measure of the arc (arc ABC). If arc ABC = 210°, then ∠AOC = 210° / 2 = 105°.

Front

If the measure of arc ABC is 210°, what is the measure of ∠AOC?

Back

150°

Front

What is the formula to find the measure of an inscribed angle in a circle?

Back

The measure of an inscribed angle is half the measure of the intercepted arc.

Front

Solve for the missing angle if the inscribed angle measures 90°. What is the measure of the intercepted arc?

Back

The intercepted arc measures 180°.

Front

What is the measure of angle A if the measure of arc PQ is 71°?

Back

The measure of angle A is 35.5° (half of 71°).

Front

If angle R measures 32°, what is the measure of the arc it intercepts?

Back

The measure of the intercepted arc is 64° (double the inscribed angle).

Front

What is the measure of angle A if the measure of arc AB is 112°?

Back

The measure of angle A is 56° (half of 112°).

Front

If the measure of arc PQ is 161°, what is the measure of the angle formed at the center of the circle?

Back

The measure of the angle formed at the center is 161°.

Front

What is the measure of an angle formed by two chords that intersect inside a circle?

Back

The measure of the angle is the average of the measures of the arcs intercepted by the angle and its vertical angle.

Front

If the measure of arc XY is 270°, what is the measure of the angle formed at the center of the circle?

Back

The measure of the angle formed at the center is 270°.