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

Explanation:

Step1: Recall degree - radian conversion formula

To convert degrees to radians, use the formula $\text{radians}=\frac{\pi}{180}\times\text{degrees}$.

Step2: Convert 125° to radians

$\text{radians}=\frac{\pi}{180}\times125=\frac{125\pi}{180}=\frac{25\pi}{36}$.

Step3: Compare with given ranges

We know that $\frac{\pi}{2}=\frac{18\pi}{36}$ and $\pi=\frac{36\pi}{36}$. Since $\frac{18\pi}{36}<\frac{25\pi}{36}<\frac{36\pi}{36}$, the angle in radians is in the range of $\frac{\pi}{2}$ to $\pi$ radians.

Answer:

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