The diagram below shows circle 0 with radii OA and OB. The length of a radius is 6

inches and the length of arc AB is 13 inches.

6

What is the measure of angle AOB to the nearest degree?

124°

Step-by-step explanation:

We are to solve for the central angle.

In the question,

We are given

The length of the radius or radius = 6 inches

The length of the arc or the arc length (AB) = 13 inches

The formula for the Arc length of a circle = 2πr * (central angle in degree : 360)

From the above formula, we can derive our formula for the measure of the central angle.

The formula for the measure of the central angle AOB = (Arc length * 360) : 2πr

Angle AOB = (13 inches * 360) : 2 * π * 6 inches

Angle AOB = 4680 : 37.699111843

Angle AOB = 124.14083392°

Approximately Angle AOB to the nearest degree = 124°

Therefore, the measure of angle AOB to the nearest degree = 124°