Topic 72 Central Angles and Arc Measures

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 extend to the circle's circumference.

Front

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

Back

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

Front

Define congruent arcs.

Back

Congruent arcs are arcs that have the same measure and are part of the same or different circles.

Front

What is the formula to find the measure of an arc?

Back

The measure of an arc can be found using the formula: Arc Measure = (Central Angle Measure) in degrees.

Front

If two arcs are congruent, what can be said about their central angles?

Back

If two arcs are congruent, their corresponding central angles are also congruent.

Front

What is the measure of a semicircle?

Back

The measure of a semicircle is 180 degrees.

Front

How do you find the length of an arc?

Back

The length of an arc can be calculated using the formula: Arc Length = (Central Angle/360) x (2πr), where r is the radius.

Front

What are concentric circles?

Back

Concentric circles are circles that share the same center but have different radii.

Front

What is the measure of arc AB if the central angle AOB is 142°?

Back

The measure of arc AB is 142°.

Front

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

Back

The measure of ∠AOC is 105°.