Central angles and arcs flashcardziz

Front

What is a central angle?

Back

A central angle is an angle whose vertex is at the center of a circle and whose sides are radii that intersect the circle.

Front

How do you calculate the measure of a central angle?

Back

The measure of a central angle is equal to the measure of the arc it intercepts.

Front

What is an arc in a circle?

Back

An arc is a portion of the circumference of a circle.

Front

What is the relationship between the central angle and the arc length?

Back

The length of an arc is directly proportional to the measure of the central angle.

Front

If the measure of arc AB is 140°, what is the measure of the central angle AOB?

Back

The measure of the central angle AOB is also 140°.

Front

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

Back

Arc length = (central angle/360) × 2πr, where r is the radius.

Front

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

Back

The measure of arc AOC is 150° (360° - 210°).

Front

What is the measure of a semicircle?

Back

The measure of a semicircle is 180°.

Front

How do you find the measure of an inscribed angle?

Back

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

Front

If the measure of arc WYZ is 231°, what is the measure of the inscribed angle XYZ?

Back

The measure of the inscribed angle XYZ is 115.5° (231°/2).