Question

a central angle of a circle divides the circle into a minor arc and a major arc where the sides of the angle intersect with the circle.

• the measure of the minor arc is equal to the measure of the central angle.
• the measure of the major arc is equal to the measure of the whole circle (360°) minus the measure of the minor arc.

use the explore tool to draw central angle zou. then, answer the questions.
the measure of minor arc zu is
the measure of major arc zvu is

Explanation:

Step1: Find the measure of minor arc \( ZU \)

Since the measure of the minor arc is equal to the measure of the central angle. If the central angle \( \angle ZOU = 60^{\circ}\), then the measure of minor arc \( ZU\) is \( 60^{\circ}\)

Step2: Find the measure of major arc \( ZVU\)

The measure of the major arc is equal to \( 360^{\circ}\) minus the measure of the minor arc.
If the minor arc \( ZU = 60^{\circ}\), then the measure of major arc \( ZVU=360^{\circ}- 60^{\circ}=300^{\circ}\)

Answer:

The measure of minor arc \( ZU\) is \( 60^{\circ}\). The measure of major arc \( ZVU\) is \( 300^{\circ}\)