Question

What is the measure of the central angle of a circle with radius $18\mathrm{cm}$ that intercepts a $12\mathrm{\pi }\mathrm{cm}$ arc?

Answer 1

Finding the measure of the central angle of the circle using Central Angle Formula :

Let $\theta$ denote the central angle of the circle.

Let $r$ denote the radius of the circle.

According to the formula, $\theta =\frac{\mathrm{Arc}\mathrm{length}\times 360°}{2\pi r}$

Calculate the measure of the central angle as shown:

$\begin{array}{rcl}\theta & =& \frac{12\mathrm{\pi }\times 360°}{2\mathrm{\pi }\times 18}\\ & =& \frac{6\times 360°}{18}\\ \therefore \theta & =& 120°\end{array}$

Therefore, the measure of the central angle of the circle is $120°$.