Question

find the radian measure of the angle with the given degree measure. 157.5°

Explanation:

Step1: Recall conversion formula

To convert degrees to radians, use the formula $x^{\circ}=x\times\frac{\pi}{180}\text{ rad}$.

Step2: Substitute the given value

Substitute $x = 157.5$ into the formula: $157.5\times\frac{\pi}{180}$.

Step3: Simplify the expression

$157.5=\frac{1575}{10}=\frac{315}{2}$, so $\frac{315}{2}\times\frac{\pi}{180}=\frac{315\pi}{360}$. Simplifying $\frac{315\pi}{360}$ by dividing both numerator and denominator by 45 gives $\frac{7\pi}{8}$.

Answer:

$\frac{7\pi}{8}$