Central Angle and Arc

If the arc length is 10 cm and the radius is 4 cm, what is the measure of the central angle in degrees?

• 60.75 degrees

• 45.57 degrees

• 30.25 degrees

• 90.12 degrees

Explain how the central angle and the arc length are related in a circle.

• The central angle and the arc length are inversely proportional in a circle.

• The central angle and the arc length are directly proportional in a circle.

• The central angle has no effect on the arc length in a circle.

• The arc length is always equal to the circumference of the circle.

Determine the central angle measure when the arc length is 15 cm and the radius is 6 cm.

• 60 degrees

• 30 degrees

• 45 degrees

• 90 degrees

Why is the central angle important when calculating the arc length of a circle?

• The central angle helps in determining the fraction of the total circumference that the arc length represents.

• The central angle is used to find the diameter of the circle

• The arc length is always equal to the circumference of the circle

• The central angle is irrelevant in calculating the arc length of a circle

If the central angle is 45 degrees and the radius is 10 cm, what is the length of the arc intercepted by this angle?

• 5.67891 cm

• 12.34567 cm

• 7.85398 cm

• 8.76543 cm

Find the value of x

• x=9

• x=14

• x=15

• x=10

Find the value of x and each arc measure.

• x=17, m DE=167°, m EF= 14°, m DFG= 346°

• x=17, m DE=167°, m EF= 43°, m DFG= 327°

• x=16, m DE=157°, m EF= 23°, m DFG= 347°

• x=16, m DE=167°, m EF= 13°, m DFG= 347°

Find the value of x and each arc measure.

• x=21, m GK=170°, m HJ= 98°, m HGJ= 259°, m GKJ= 201°

• x=21, m GK=167°, m HJ= 98°, m HGJ= 262°, m GKJ= 201°

• x=22, m GK=167°, m HJ= 98°, m HGJ= 262°, m GKJ= 201°

• x=22, m GK=167°, m HJ= 97°, m HGJ= 263°, m GKJ= 201°

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

• 7/4π

• 7/2π

• 1/8π

• 45π

Alison is jogging on a circular track that has a radius of 140 feet.  She runs along the track from point R to point N, a distance of 230 feet. Find to the nearest degree, the measure of minor arc RN.

• 47

• 74

• 94

• 123