Central Angles and Arc Length in a Circle

Determine the value of x.

• 80

• 120

• 160

• 200

If the measure of arc ABC = 210°, what is the measure of arc AC?

• 150°

• 100°

• 210°

• 105°

The measure of an arc is equal to the measure of the central angle that intercepts the arc. Find x.

• x = 160

• x = 40

• x = 80

• x = 360

Find the measure of arc JKM

When she is outdoors, Tasha, the dog, is tied to a stake in the center of a circular area of radius 24 feet. The angle between her dog house and her favorite hydrant is 165 degrees.  What is the length of the arc from her dog house to the hydrant, following minor arc DG, to the nearest foot.

• 40

• 35

• 55

• 69

FIND THE ARC LENGTH OF THE BOLDED ARC

• A

• B

• C

• D

Find the arc length.  Leave your answer in terms of π.

• 7/4π

• 7/2π

• 1/8π

• 45π

Lin thinks that the central angle in circle A is

congruent to the central angle in circle B. Do you

agree with Lin? Show or explain your reasoning.

• I agree. The ratios of the arc length to the radius are equivalent.

• I disagree. The ratios of the arc length to radius are not equivalent.

Find the arc length.  Leave your answer in terms of π.

• 7/4π

• 7/2π

• 1/8π

• 45π

Lin thinks that the central angle in circle A is congruent to the central angle in circle B. Do you agree with Lin? Show or explain your reasoning.

• I agree. The ratios of the arc length to the radius are equivalent.

• I disagree. The ratios of the arc length to radius are not equivalent.