Question

if $overline{ef}congoverline{eh}$ and $mangle egf = 64^{circ}$, what is $mangle egh$?
$mangle egh=square^{circ}$

Explanation:

Step1: Recall congruent - triangle property

Since $\overline{EF}\cong\overline{EH}$, $\angle EFG = \angle EHG=90^{\circ}$ and $EG = EG$ (common side), right - triangles $\triangle EFG$ and $\triangle EHG$ are congruent by the Hypotenuse - Leg (HL) congruence criterion.

Step2: Use congruent - angle property

In congruent triangles $\triangle EFG$ and $\triangle EHG$, corresponding angles are equal. So, $\angle EGF=\angle EGH$.

Step3: Find the measure of $\angle EGH$

Given that $m\angle EGF = 64^{\circ}$, then $m\angle EGH=64^{\circ}$.

Answer:

$64$