Question

question 10 of 10 what is the measure of ∠xyz? a. 54° b. 108° c. 33° d. 75°

Explanation:

Step1: Recall the angle - at - the - intersection - of - chords formula

The measure of an angle formed by two chords intersecting inside a circle is given by $\frac{1}{2}$ the sum of the measures of the intercepted arcs.
Let the two intercepted arcs be $33^{\circ}$ and $75^{\circ}$.

Step2: Apply the formula

$m\angle XYZ=\frac{1}{2}(33^{\circ}+75^{\circ})$.
First, calculate the sum inside the parentheses: $33 + 75=108$.
Then, divide by 2: $\frac{108^{\circ}}{2}=54^{\circ}$.

Answer:

A. $54^{\circ}$