Given a circle with center O, if arcs XY and YZ are congruent, what is the measure...
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Problem
Given a circle with center O, if arcs XY and YZ are congruent, what is the measure of angle YOZ?
Step-by-step solution
The arc XZ is given as 80 degrees. Since arcs XY and YZ are congruent, and the total degrees in a circle is 360, the remaining arc is 360 - 80 = 280 degrees. This 280 degrees is split equally between arc XY and arc YZ, so each is 140 degrees. The angle YOZ is the central angle subtending arc YZ. Therefore, the measure of angle YOZ is equal to the measure of arc YZ, which is 140 degrees.
Answer
$140^{\circ}$