Question

what is m∠fgh?
h
39
i
39
41°
g
f
m∠fgh = □°

Explanation:

Step1: Use the Hypotenuse - Leg (HL) Congruence Theorem

Since \(GI = GI\) (common side), \(GH = GF\) (both lengths are 39), and \(\angle H=\angle F = 90^{\circ}\), by the HL theorem, \(\triangle GHI\cong\triangle GFI\).

Step2: Find the measure of \(\angle FGH\)

Because \(\triangle GHI\cong\triangle GFI\), \(\angle HGI=\angle FGI\). Given \(\angle FGI = 41^{\circ}\), then \(m\angle FGH=\angle HGI+\angle FGI\). So \(m\angle FGH = 41^{\circ}+ 41^{\circ}\).

Answer:

\(82\)