A circle has a circumference of / blue{6}6start color #6495ed, 6, end color #6495ed. It has an arc of length / dfrac{17}{3}

3

17



start fraction, 17, divided by, 3, end fraction.

What is the central angle of the arc, in degrees?

The central angle of the arc is 340°

Step-by-step explanation:

The formula for calculating the area of an arc = theta/360° * 2πr

Note that circumference of the circle = 2πr

The area of an arc = theta/360° * circumference of the circle

Given length of the arc = 17/3

Circumference of the circle = 2πr = 6

On substitution;

17/3 = theta/360 * 6

17/3 = theta/60

Cross multiplying;

3theta = 17*60

theta = 17*60/3

theta = 17*20

theta = 340°