Question

if $overline{wx}=overline{wz}$, $mangle wyx = 2p + 37^{circ}$, and $mangle wyz = 4p - 5^{circ}$, what is $mangle wyz$?
$mangle wyz=square^{circ}$

Explanation:

Step1: Set the angle measures equal

Since $\overline{WX}=\overline{WZ}$ and $WY$ is a common - side, and the right - angles are equal, by the Hypotenuse - Leg (HL) congruence criterion, $\triangle WYX\cong\triangle WYZ$. So, $m\angle WYX = m\angle WYZ$.
$2p + 37=4p - 5$

Step2: Solve for $p$

Subtract $2p$ from both sides of the equation:
$37=4p - 2p-5$
$37 = 2p-5$
Add 5 to both sides:
$2p=37 + 5$
$2p=42$
Divide both sides by 2:
$p = 21$

Step3: Find $m\angle WYZ$

Substitute $p = 21$ into the expression for $m\angle WYZ$:
$m\angle WYZ=4p - 5$
$m\angle WYZ=4\times21-5$
$m\angle WYZ=84 - 5$
$m\angle WYZ = 79$

Answer:

$79$