Question

if $overline{wz}congoverline{yz}$, $mangle wxz = p + 52^{circ}$, and $mangle yxz = 3p$, what is $mangle yxz?

mangle yxz=square^{circ}$

Explanation:

Step1: Use congruent - side property

Since $\overline{WZ}\cong\overline{YZ}$ and $\angle W$ and $\angle Y$ are right - angles, and $ZX$ is common, by the Hypotenuse - Leg (HL) congruence criterion, $\triangle WZX\cong\triangle YZX$. So, $\angle WXZ=\angle YXZ$.

Step2: Set up the equation

Set up the equation $p + 52^{\circ}=3p$.

Step3: Solve for $p$

Subtract $p$ from both sides: $52^{\circ}=3p - p$, which simplifies to $52^{\circ}=2p$. Then divide both sides by 2: $p = 26^{\circ}$.

Step4: Find $m\angle YXZ$

Since $m\angle YXZ = 3p$, substitute $p = 26^{\circ}$ into the expression. So, $m\angle YXZ=3\times26^{\circ}=78^{\circ}$.

Answer:

$78$