Question

what is m∠egf? m∠egf = (square^{circ})

Explanation:

Step1: Identify congruent triangles

Triangles $\triangle EHG$ and $\triangle EFG$ are right - angled triangles with $EG$ as a common hypotenuse and $EH = EF$ (marked with equal segments). By the Hypotenuse - Leg (HL) congruence criterion, $\triangle EHG\cong\triangle EFG$.

Step2: Use congruent - angle property

Since $\triangle EHG\cong\triangle EFG$, corresponding angles are equal. $\angle HGE=\angle FGE$. Given $\angle HGE = 36^{\circ}$, then $\angle EGF=\angle HGE = 36^{\circ}$.

Answer:

$36$