Central Angles, Arc Measure, and Arc Length

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

How is the measure of an arc related to its central angle?

Back

The measure of an arc is equal to the measure of its central angle, measured in degrees.

Front

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

Back

Arc Length = (Central Angle/360) x 2πr, where r is the radius of the circle.

Front

If the central angle is 90 degrees, what fraction of the circle does the arc represent?

Back

The arc represents 1/4 of the circle.

Front

What is the relationship between the degree measure of an arc and the circle's circumference?

Back

The degree measure of an arc is a fraction of the total 360 degrees of the circle, which corresponds to the fraction of the circle's circumference.

Front

How do you convert arc length to degrees?

Back

To convert arc length to degrees, use the formula: Degrees = (Arc Length / Circumference) x 360.

Front

What is the circumference of a circle with a radius of 5 cm?

Back

Circumference = 2πr = 2π(5) = 10π cm or approximately 31.42 cm.

Front

If an arc length is 15.71 cm, what is the central angle in degrees for a circle with a radius of 5 cm?

Back

Central Angle = (Arc Length / Circumference) x 360 = (15.71 / 31.42) x 360 = 180 degrees.

Front

What is the measure of arc AXB if the central angle is 100 degrees?

Back

The measure of arc AXB is 100 degrees.

Front

If the measure of arc TVW is 267 degrees, what is the remaining arc measure in the circle?

Back

The remaining arc measure is 360 - 267 = 93 degrees.