Question

the difference between the measure of angle a and the measure of angle b is -\frac{5}{12}\pi radians. which expression shows the difference between the measure of angle a and the measure of angle b, in degrees? a. -\frac{5}{12}\pi\cdot\frac{180}{\pi} b. -\frac{5}{12}\pi\cdot\frac{\pi}{180} c. -\frac{5}{12}\pi\cdot\frac{180}{\pi} d. -\frac{5}{12}\pi\cdot\frac{360}{\pi}

Explanation:

Step1: Recall the conversion formula

To convert radians to degrees, use the formula $1\ radian=\frac{180^{\circ}}{\pi}$.

Step2: Convert the given radian - measure to degrees

Given the angle $B =-\frac{5}{12}\pi$ radians. Multiply by $\frac{180^{\circ}}{\pi}$ to convert to degrees. So, $-\frac{5}{12}\pi\times\frac{180^{\circ}}{\pi}$. The $\pi$ terms cancel out, and $-\frac{5\times180}{12}=- 75^{\circ}$.

Answer:

b. $-\frac{5}{12}\pi\cdot\frac{180}{\pi}$