Arc Measure and Arc Length

Front

What is the measure of a minor arc in a circle?

Back

The measure of a minor arc is the measure of the central angle that subtends the arc, expressed in degrees.

Front

How do you find the measure of a major arc?

Back

The measure of a major arc can be found by subtracting the measure of the minor arc from 360 degrees.

Front

What is the formula for arc length?

Back

Arc Length = (θ/360) * 2πr, 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 degrees, what is the arc length?

Back

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

Front

Define a central angle in relation to arcs.

Back

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

Front

What is the relationship between the measures of a minor arc and its corresponding central angle?

Back

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

Front

How do you calculate the measure of an arc given its length?

Back

To find the measure of an arc, use the formula: Measure of Arc = (Arc Length / (2πr)) * 360.

Front

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

Back

A minor arc is less than 180 degrees, while a major arc is greater than 180 degrees.

Front

If arc AB measures 135 degrees, what is the measure of the major arc ADB?

Back

The measure of the major arc ADB is 360 - 135 = 225 degrees.

Front

What is the significance of leaving the answer in terms of π when calculating arc length?

Back

Leaving the answer in terms of π provides an exact value rather than a decimal approximation.