Circles Exercises

Suppose an inscribed angle has a measure of 68°. What is the measure of the arc it intercepts?

Hint

Take a look at the Inscribed Angle Theorem.

An inscribed angle has a measure of 160°. What is the measure of the arc it intercepts?

Hint

What does the Inscribed Angle Theorem say?

An inscribed angle has a measure of 13°. What is the measure of the arc it intercepts?

Hint

Seriously, it's all about the Inscribed Angle Theorem.

An inscribed angle intercepts an arc of 124°. What is the measure of the inscribed angle?

Hint

This time, we know the measure of the arc, but not the inscribed angle.

An inscribed angle intercepts an arc of 180°. What is the measure of the inscribed angle?

Hint

We're trying to find out the measure of the inscribed angle, not the arc.

An inscribed angle intercepts an arc of 95°. What is the measure of the inscribed angle?

Hint

You've probably memorized the Inscribed Angle Theorem by now.

In the figure below, points A, B, C, and D are on the circle. If m∠ADC = 90° and mAB = 84°, what is m∠CDB?

Hint

You'll need arc addition and the Inscribed Angle Theorem.

In the figure below, points A, B, C, and D are on ⊙O and m∠ABC = 150°. What is m∠AOC?

Hint

Notice that ∠ABC is an inscribed angle that intercepts arc ADC.