Questions: What is the measure of angle XYZ? A. 108° B. 75° C. 54° D. 33°

Solution Steps

The measure of arc VW is 33°. The measure of arc WX is 75°. Therefore, the measure of arc VXW is the sum of the measures of arc VW and arc WX. Arc VXW = Arc VW + Arc WX Arc VXW = 33° + 75° Arc VXW = 108°

The inscribed angle XYZ intercepts the arc VXW. The measure of an inscribed angle is half the measure of its intercepted arc. $\angle XYZ = \frac{1}{2} \text{Arc VXW}$ $\angle XYZ = \frac{1}{2} (108^{\circ})$ $\angle XYZ = 54^{\circ}$

Final Answer