Question

in the diagram of circle a, what is the measure of ∠xyz? 35° 70° 75° 140°

Explanation:

Step1: Find the measure of the intercepted arc

The measure of the major arc $WXZ$ is $175^{\circ}$ and the measure of the minor arc $WX$ is $105^{\circ}$, so the measure of the arc $XZ$ is $360^{\circ}-175^{\circ}- 105^{\circ}=80^{\circ}$.

Step2: Apply the tangent - secant angle formula

The measure of an angle formed by a tangent and a secant is half the difference of the measures of the intercepted arcs. The formula is $\angle XYZ=\frac{1}{2}(\text{major arc}-\text{minor arc})$. Here, the major arc is $175^{\circ}$ and the minor arc is $105^{\circ}$. So $\angle XYZ=\frac{1}{2}(175^{\circ}- 105^{\circ})$.

Step3: Calculate the angle measure

$\angle XYZ=\frac{1}{2}(70^{\circ}) = 35^{\circ}$.

Answer:

$35^{\circ}$