Question

Find the degree measure of the angle with the given radian measure.

$-\frac{2\pi }{15}$

Short answer

$\mathbf{\text{-\hspace{0.17em}}}{\mathbf{24}}^{°}$

Step-by-step solution

Step 1. Given information.

The given radian measure is:

$-\frac{2\pi }{15}$rad.

Step 2. Explanation.

We know that

$1\text{\hspace{0.17em}radian\hspace{0.17em}=\hspace{0.17em}}\left(\frac{{180}^{\circ }}{\pi }\right)$

Thus to find the degrees of the angle multiply the radian measure with$\left(\frac{{180}^{\circ }}{\pi }\right)$

Here the radian measure $\mathrm{\pi }$is not available so when we multiply put$\pi =3.14$

Step 3. Calculation.

To convert radians to degrees, multiply by$\left(\frac{{180}^{\circ }}{\pi }\right)$:

$-\frac{2\pi }{15}\text{rad}=-\left(\frac{2\pi }{15}\text{\hspace{0.17em}x\hspace{0.17em}}\frac{180}{\pi }\right)$

Put $\pi =3.14$in the expression, we get:

$\begin{array}{l}=-{\left(\frac{2x3.14}{15}x\frac{180}{3.14}\right)}^{{}^{\circ }}\\ =-{\left(\frac{360}{15}\right)}^{{}^{\circ }}\\ =-{24}^{{}^{\circ }}\end{array}$