Question

in the diagram of circle p, $m\angle xyz$ is $72^\circ$. what is the value of $x$?$\bigcirc$ $108^\circLXB0\bigcirc$ $216^\circ$$\bigcirc$ $252^\circ$

Explanation:

Step1: Recall exterior angle theorem

The measure of an angle formed by two secants outside a circle is half the difference of the measures of the intercepted arcs.
$\angle XYZ = \frac{1}{2}[(360 - x) - x]$

Step2: Substitute known angle value

Plug $m\angle XYZ = 72^\circ$ into the formula.
$72 = \frac{1}{2}(360 - x - x)$

Step3: Simplify and solve for x

First multiply both sides by 2, then solve for x.
$144 = 360 - 2x$
$2x = 360 - 144$
$2x = 216$
$x = 108$

Answer:

108°