in the diagram of circle p, m∠xyz is 72°. what is the value of x? 108° 144° 216° 252°

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. Here, the inscribed angle $\angle XYZ = 72^{\circ}$, and the intercepted arc is $(360 - x)^{\circ}$.

Step2: Set up the equation

According to the inscribed - angle theorem, $m\angle XYZ=\frac{1}{2}(360 - x)$. Substitute $m\angle XYZ = 72^{\circ}$ into the equation: $72=\frac{1}{2}(360 - x)$.

Step3: Solve the equation for $x$

First, multiply both sides of the equation by 2: $2\times72=360 - x$, so $144 = 360 - x$. Then, add $x$ to both sides: $144+x=360$. Finally, subtract 144 from both sides: $x = 360 - 144=216$.

Answer:

$216^{\circ}$