Central Angles and Arcs Quick Check

Front

Define a minor arc.

Back

A minor arc is an arc that is smaller than a semicircle, typically defined by two endpoints on a circle.

Front

Define a major arc.

Back

A major arc is an arc that is larger than a semicircle, defined by two endpoints on a circle and includes the longer path between them.

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

If the measure of arc AB is 80°, what is the measure of the central angle AOB?

Back

The measure of the central angle AOB is also 80°.

Front

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

Back

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

Front

What is the formula to find the area of a sector?

Back

Area of a sector = (θ/360) × πr², where θ is the central angle in degrees and r is the radius.

Front

If the radius of a circle is 10 cm and the central angle is 60°, what is the length of the arc?

Back

Arc length = (60/360) × 2π(10) = (1/6) × 20π = (10π/3) cm.

Front

If the radius of a circle is 5 cm and the central angle is 90°, what is the area of the sector?

Back

Area of the sector = (90/360) × π(5)² = (1/4) × 25π = (25π/4) cm².

Front

What is the measure of a semicircle?

Back

The measure of a semicircle is 180°.

Front

If arc CD measures 150°, what is the measure of the corresponding minor arc?

Back

The corresponding minor arc is 150°.