Question

an arc on a circle measures $250^\circ$. within which range is the radian measure of the central angle?
0 to $\frac{\pi}{2}$ radians
$\frac{\pi}{2}$ to $\pi$ radians
$\pi$ to $\frac{3\pi}{2}$ radians
$\frac{3\pi}{2}$ to $2\pi$ radians

Explanation:

Step1: Convert degrees to radians

Use conversion formula: $\text{Radians} = \text{Degrees} \times \frac{\pi}{180}$
$250^\circ \times \frac{\pi}{180} = \frac{25\pi}{18} \approx 4.363$ radians

Step2: Define range values

Calculate radian range bounds:
$\pi \approx 3.142$, $\frac{3\pi}{2} \approx 4.712$, $2\pi \approx 6.283$

Step3: Compare to find range

Check where $\frac{25\pi}{18}$ falls:
$\pi < \frac{25\pi}{18} < \frac{3\pi}{2}$

Answer:

$\pi$ to $\frac{3\pi}{2}$ radians