Question

an arc on a circle measures 125°. 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{3\pi}{2} radians
\frac{3\pi}{2} to 2\pi radians

Explanation:

Step1: Convert degree to radian

Use the formula \( radian=\frac{\pi}{180}\times degree \).
For \( 125^{\circ} \), we have \( \frac{\pi}{180}\times125=\frac{125\pi}{180}=\frac{25\pi}{36}\approx2.18 \).

Step2: Compare with given ranges

We know that \( \frac{\pi}{2}\approx1.57 \), \( \pi\approx3.14 \).
Since \( 1.57<2.18<3.14 \), and \( \frac{\pi}{2}<\frac{25\pi}{36}<\pi \).

Answer:

\(\frac{\pi}{2}\) to \(\pi\) radians