Inscribed Angles

Front

What is an inscribed angle?

Back

An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. The vertex of the angle is on the circle, and the sides of the angle are the chords.

Front

What is the relationship between an inscribed angle and the arc it intercepts?

Back

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

Front

If the measure of arc AB is 80°, what is the measure of the inscribed angle ACB?

Back

40° (since the inscribed angle is half of the intercepted arc).

Front

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

Back

Measure of inscribed angle = 1/2 * measure of intercepted arc.

Front

How do you find the measure of an arc given the inscribed angle?

Back

Measure of intercepted arc = 2 * measure of inscribed angle.

Front

If angle ACB measures 30°, what is the measure of arc AB?

Back

60° (since the arc is twice the inscribed angle).

Front

What is the measure of an angle inscribed in a semicircle?

Back

The measure of an angle inscribed in a semicircle is always 90°.

Front

What is the significance of the vertex of an inscribed angle?

Back

The vertex of an inscribed angle must lie on the circle for the angle to be considered inscribed.

Front

Can an inscribed angle intercept more than one arc?

Back

No, an inscribed angle can only intercept one arc at a time.

Front

What is the relationship between two inscribed angles that intercept the same arc?

Back

Two inscribed angles that intercept the same arc are equal in measure.