Finding Inscribed Angle Measure in a Circle
The image depicts a circle with a central angle ∠XZY measuring 144° and an inscribed angle ∠YZV that intercepts the same arc XY as the central angle.
According to the inscribed angle theorem, the measure of an inscribed angle is half the measure of the central angle that intercepts the same arc. Therefore, to find the measure of angle ∠YZV, we simply need to take half of the measure of ∠XZY.
∠XZY = 144°
∠YZV = 1/2 × ∠XZY
∠YZV = 1/2 × 144°
∠YZV = 72°
So, the measure of ∠YZV is 72 degrees.
