Question

how many degrees is $\frac{15}{16}pi$ radians?
84.375°
93.75°
168.75°
337.5°

Explanation:

Step1: Recall conversion formula

We know that $\pi$ radians $ = 180^{\circ}$. So to convert $\frac{15}{16}\pi$ radians to degrees, we use the proportion. Let $x$ be the angle in degrees. Then $\frac{x}{180}=\frac{\frac{15}{16}\pi}{\pi}$.

Step2: Simplify the equation

Since $\frac{\frac{15}{16}\pi}{\pi}=\frac{15}{16}$, our equation becomes $x = 180\times\frac{15}{16}$.

Step3: Calculate the value of $x$

$180\times\frac{15}{16}=\frac{180\times15}{16}=\frac{2700}{16}=168.75$.

Answer:

$168.75^{\circ}$