Arcs and Central Angles

Front

What is an arc in a circle?

Back

An arc is a portion of the circumference of a circle, defined by two endpoints on the circle.

Front

What is a central angle?

Back

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

Front

How do you calculate the measure of an arc?

Back

The measure of an arc is equal to the measure of the central angle that subtends it.

Front

What is a minor arc?

Back

A minor arc is an arc that measures less than 180 degrees.

Front

What is a major arc?

Back

A major arc is an arc that measures more than 180 degrees.

Front

If the measure of arc AB is 142°, what is the measure of the central angle ∠AOB?

Back

The measure of the central angle ∠AOB is also 142°.

Front

What is the relationship between the measures of arcs and their corresponding central angles?

Back

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

Front

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

Back

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

Front

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

Back

Length of arc = (θ/360) × 2πr, where θ is the central angle in degrees and r is the radius.

Front

What is the difference between a semicircle and a minor arc?

Back

A semicircle is an arc that measures exactly 180°, while a minor arc measures less than 180°.