in the diagram of circle a, what is the measure of ∠xyz? 35° 70° 75° 140°
in the diagram of circle a, what is the measure of ∠xyz? 35° 70° 75° 140°
Answer
Answer:
35°
Explanation:
Step1: Recall the inscribed - angle formula
The measure of an inscribed angle is half the measure of its intercepted arc. The measure of the arc $WZ$ is $175^{\circ}+ 105^{\circ}=280^{\circ}$. The measure of the other arc (the arc intercepted by $\angle XYZ$) is $360^{\circ}-280^{\circ} = 80^{\circ}$.
Step2: Apply the inscribed - angle formula
Let $\theta$ be the measure of $\angle XYZ$. Then $\theta=\frac{1}{2}(175 - 105)$. [ \begin{align*} \theta&=\frac{1}{2}(70)\ \theta& = 35^{\circ} \end{align*} ]