Question

explore the area of sectors of circles by following these steps.

the ratio of the central angle measure to the measure of the entire circle is now 1/2.

the area of the sector created by central angle acb is 1/2 the area of the entire circle because the central angle is 1/2 the measure of the entire circle.

1. move point a to create a central angle of 90°.

the ratio of the central angle measure to the measure of the entire circle is
options: 1/12, 1/4, 1/2

m∠acb = 90°
(image of a circle with center c, radius cb = 3, sector acb shaded, ∠acb = 90°)

Explanation:

Step1: Recall the total degrees in a circle

A full circle has a measure of \( 360^\circ \).

Step2: Calculate the ratio

The central angle here is \( 90^\circ \). To find the ratio of the central angle to the full circle, we divide the central angle by the total degrees in a circle: \( \frac{90^\circ}{360^\circ} = \frac{1}{4} \).

Answer:

\( \frac{1}{4} \) (corresponding to the option "1/4")