Question

1. one half of circle a has been divided into 3 equal parts. label points e and f with the radian measures of angles eap and fap. then write the corresponding degree measure for each angle.

Explanation:

Step1: Find the measure of each part in radians

The half - circle has a measure of \(\pi\) radians. Since it is divided into 3 equal parts, each part has a measure of \(\frac{\pi}{3}\) radians.

Step2: Calculate the radian measure of \(\angle EAP\)

\(\angle EAP = 2\times\frac{\pi}{3}=\frac{2\pi}{3}\) radians.

Step3: Calculate the degree measure of \(\angle EAP\)

Using the conversion formula \(1\) radian \(=\frac{180^{\circ}}{\pi}\), for \(\theta=\frac{2\pi}{3}\) radians, \(\theta=\frac{2\pi}{3}\times\frac{180^{\circ}}{\pi}=120^{\circ}\)

Step4: Calculate the radian measure of \(\angle FAP\)

\(\angle FAP=\frac{\pi}{3}\) radians.

Step5: Calculate the degree measure of \(\angle FAP\)

Using the conversion formula \(1\) radian \(=\frac{180^{\circ}}{\pi}\), for \(\theta = \frac{\pi}{3}\) radians, \(\theta=\frac{\pi}{3}\times\frac{180^{\circ}}{\pi}=60^{\circ}\)

Answer:

• Radian measure of \(\angle EAP\): \(\frac{2\pi}{3}\), Degree measure of \(\angle EAP\): \(120^{\circ}\)
• Radian measure of \(\angle FAP\): \(\frac{\pi}{3}\), Degree measure of \(\angle FAP\): \(60^{\circ}\)