Angles in Circles

Front

What is the measure of arc DE if the central angle is 80°?

Back

Arc DE = 64° (Arc length is proportional to the central angle).

Front

An angle whose vertex is the center of a circle is a(n) ______.

Back

Central angle.

Front

Solve for x if the inscribed angle is 40° and the arc it intercepts is x.

Back

x = 80° (Inscribed angle is half the measure of the intercepted arc).

Front

Determine the measure of ∠NOP if it intercepts an arc of 40°.

Back

∠NOP = 20° (Inscribed angle is half the measure of the intercepted arc).

Front

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

Back

Inscribed angle.

Front

If the central angle is 90°, what is the measure of the intercepted arc?

Back

The intercepted arc measures 90°.

Front

What is the relationship between a central angle and its intercepted arc?

Back

The measure of the central angle is equal to the measure of its intercepted arc.

Front

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

Back

The inscribed angles are equal.

Front

What is the measure of an inscribed angle that intercepts an arc of 100°?

Back

The inscribed angle measures 50° (Inscribed angle is half the intercepted arc).

Front

What is the formula for finding the length of an arc?

Back

Arc length = (θ/360) * 2πr, where θ is the central angle in degrees and r is the radius.