Question

an arc on a circle measures 85°. the measure of the central angle, in radians, is within which range? 0 to $\frac{pi}{2}$ radians $\frac{pi}{2}$ to $pi$ radians $pi$ to $\frac{3pi}{2}$ radians $\frac{3pi}{2}$ to $pi$ radians

Explanation:

Step1: Recall degree - radian conversion formula

We know that to convert degrees to radians, we use the formula $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$.

Step2: Convert 85 degrees to radians

$\theta = 85\times\frac{\pi}{180}=\frac{85\pi}{180}=\frac{17\pi}{36}$.

Step3: Compare with given ranges

We know that $\frac{\pi}{2}=\frac{18\pi}{36}$ and $0 < \frac{17\pi}{36}<\frac{18\pi}{36}=\frac{\pi}{2}$.

Answer:

0 to $\frac{\pi}{2}$ radians