Question

if (overline{fi}congoverline{hi}) and (mangle hgi = 49^{circ}), what is (mangle fgi)?(mangle fgi=square^{circ})

Explanation:

Step1: Use Hypotenuse - Leg Congruence

Since \(FI\cong HI\) and \(GI = GI\) (common side), and \(\angle GFI=\angle GHI = 90^{\circ}\), by Hypotenuse - Leg (\(HL\)) congruence, \(\triangle GFI\cong\triangle GHI\).

Step2: Use Congruent Triangles' Angles

Because \(\triangle GFI\cong\triangle GHI\), then \(\angle FGI=\angle HGI\). Given \(m\angle HGI = 49^{\circ}\), so \(m\angle FGI=49^{\circ}\).

Answer:

\(49\)