Question

an arc on a circle measures 250°. 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 degree to radian

Use the formula \( \text{radian}=\frac{\pi}{180}\times\text{degree}\).
For \(250^{\circ}\), the radian measure is \( \frac{\pi}{180}\times250=\frac{25\pi}{18}\approx 4.36\).

Step2: Compare with given ranges

• \(0\approx0\), \(\frac{\pi}{2}\approx1.57\), \(\pi\approx3.14\), \(\frac{3\pi}{2}\approx4.71\), \(2\pi\approx6.28\).
• Since \(3.14\lt4.36\lt4.71\), that is \(\pi\lt\frac{25\pi}{18}\lt\frac{3\pi}{2}\).

Answer:

\(\pi\) to \(\frac{3\pi}{2}\) radians (the third option).