Circles: Special Angles and Arcs in Circles

Measures of Arcs

 

Since the entire circle measures 360°, if we know either the measure of the minor arc or the measure of the major arc, we simply subtract that from 360 to find the measure of the other arc.

Example:
Find the measure of arc XYZ in the figure below.

Circle with points X, Y, and Z, arc XZ is 142 degrees
Circle with points X, Y and Z

the measure of arc XYZ equals 360 minus the measure of arcXZ; the measure of XYZ equals 360 minus 142; the measure of XYZ equals 218 degrees