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

What is the measure of arc FE if inscribed angle EFD measures 27°?

Back

54° (since the arc is twice the inscribed angle).

Front

If angle ACB is 22.5°, what is the measure of arc AB?

Back

45° (since the arc is twice the inscribed angle).

Front

What is the measure of an inscribed angle that intercepts a semicircle?

Back

90° (since the intercepted arc is 180°, and half of that is 90°).

Front

If two inscribed angles intercept the same arc, what can be said about their measures?

Back

The measures of the inscribed angles are equal.

Front

What is the measure of angle E if arc DE measures 88°?

Back

44° (since the inscribed angle is half of the intercepted arc).