Question

A circle has a circumference of 10. It has an arc length of 9/2. What is the central angle of the arc in degrees?

Answer 1

Answer:

162 degrees

Step-by-step explanation:

1 / 6

The ratio between the arc's central angle θ (theta) and 360° is equal to the ratio between the arc length (s) and the circle's circumference (c).

2/6

$\frac{theta}{360 degrees}$  = $\frac{s}{c}$

3/6

$\frac{theta}{360degrees}$  = $\frac{9}{2}$ ÷ 10

4/6

$\frac{theta}{360degrees}$  =$\frac{9}{20}$

5/6

θ = $\frac{9}{20}$ × 360°

6/6

θ = 162°

Answer 2

Answer: The central angle of the arc is 162 degrees.

Step-by-step explanation: The information available are as follows;

Circumference of the circle equals 10. Length of an arc equals 9/2. The circumference of a circle is given as;

Circumference = 2Pi x r

That means 2Pi x r = 10.

Also the length of an arc along the same circle is 9/2. Length of an arc is calculated as;

Length of arc = (X/360) x 2Pi x r

Where X is the central angle of the arc

That means;

9/2 = (X/360) x 2Pi x r

We can now substitute for the known values as follows

Length of an arc = (X/360) x 2Pi x r

9/2 = (X/360) x 10

9/2 = 10X/360

By cross multiplication we now have

(9 x 360)/(2 x 10) = X

3240/20 = X

162 = X

The angle at the center of the arc is 162 degrees.