Question

an arc on a circle measures 125°. the measure of the central - angle, in radians, is within which range? 0 to 1/2 π radians 1/2 π to π radians π to 3/2 π radians 3/2 π to 2π radians

Explanation:

Step1: Convert degrees to radians

We know that to convert degrees to radians, we use the formula $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. Given $\theta_{deg} = 125^{\circ}$, then $\theta_{rad}=125\times\frac{\pi}{180}=\frac{25\pi}{36}\approx 0.694\pi$.

Step2: Determine the range

Since $0.5\pi<0.694\pi < \pi$, the angle is in the range $\frac{\pi}{2}$ to $\pi$ radians.

Answer:

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