Question

question 4 of 10
what is the measure of ∠xyz?

Explanation:

Step1: Recall angle - arc relationship

The measure of an inscribed - angle formed by two chords is half the sum of the measures of the intercepted arcs.

Step2: Identify intercepted arcs

The intercepted arcs for ∠XYZ are arc VZ and arc WX. Arc VZ = 33° and arc WX = 75°.

Step3: Calculate the measure of ∠XYZ

The formula for the measure of an angle formed by two intersecting chords is $m\angle XYZ=\frac{1}{2}(m\overset{\frown}{VZ}+m\overset{\frown}{WX})$. Substitute $m\overset{\frown}{VZ} = 33^{\circ}$ and $m\overset{\frown}{WX}=75^{\circ}$ into the formula: $m\angle XYZ=\frac{1}{2}(33 + 75)=\frac{1}{2}(108)=54^{\circ}$.

Answer:

C. 54°