Question

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 formula for angles formed by a tangent and a chord

The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc. Here, $\angle XYZ$ is an angle formed by tangent $YZ$ and chord $XZ$, and the intercepted arc is $(360 - x)^{\circ}$. The formula is $m\angle XYZ=\frac{1}{2}(360 - x)$.

Step2: Substitute the given angle measure into the formula

We know that $m\angle XYZ = 72^{\circ}$, so we have the equation $72=\frac{1}{2}(360 - x)$.

Step3: Solve the equation for $x$

First, multiply both sides of the equation by 2: $72\times2=360 - x$, which simplifies to $144 = 360 - x$.
Then, add $x$ to both sides: $144+x=360$.
Finally, subtract 144 from both sides: $x = 360 - 144=216$.

Answer:

$216^{\circ}$