Question

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

$\frac{5\pi }{18}$

Short answer

${\mathbf{50}}^{°}$

Step-by-step solution

Step 1. Given information.

The given radian measure is:

$\frac{5\pi }{18}$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$\left(\frac{{180}^{\circ }}{\pi }\right)$:

$\frac{5\pi }{18}\text{rad}=\left(\frac{5\pi }{18}\text{\hspace{0.17em}x\hspace{0.17em}}\frac{180}{\pi }\right)$

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

$\begin{array}{l}={\left(\frac{5x3.14}{18}x\frac{180}{3.14}\right)}^{\circ }\\ ={\left(\frac{5x180}{18}\right)}^{{}^{\circ }}\\ ={50}^{{}^{\circ }}\end{array}$