# Can anyone include a diagram as part of the explanation here?

Feb 28, 2017

${143}^{\circ}$

#### Explanation:

In a circle, the length of an arc is a portion of the circumference.
For example, an arc measure of ${60}^{\circ}$ is $\frac{1}{6}$ of the circle (${360}^{\circ}$). So the length of that arc will be $\frac{1}{6}$ of the circumference.

$\implies$ arc length $= 2 \cdot \pi \cdot r \cdot \left(\frac{\Theta}{360}\right)$

Given arc length $A B = 10 c m$, and radius $= 4 c m$

$\implies 10 = 2 \cdot \pi \cdot 4 \cdot \left(\frac{\Theta}{360}\right)$

$\implies \Theta = \frac{10 \cdot 360}{2 \cdot \pi \cdot 4} = {143}^{\circ}$ (to the nearest degree)