Question

if \\( \overline { f i } \cong \overline { h i } \\) and \\( m \angle h g i = 39 ^ { \circ } \\), what is \\( m \angle f g h? \\)
\\( m \angle f g h = \square ^ { \circ } \\)

Explanation:

Step1: Use Hypotenuse - Leg (HL) Congruence Theorem

Since \( \overline{FI}\cong\overline{HI}\), \( \overline{FG}\cong\overline{HG}\) (common side), and \( \angle F\cong\angle H = 90^{\circ}\), by HL theorem, \( \triangle FGI\cong\triangle HGI\).

Step2: Use Congruent Triangles Properties

If \( \triangle FGI\cong\triangle HGI\), then \( \angle FGI=\angle HGI\). Given \( m\angle HGI = 39^{\circ}\), so \( m\angle FGH=m\angle FGI + m\angle HGI\).
Since \( m\angle FGI=m\angle HGI = 39^{\circ}\), then \( m\angle FGH=39^{\circ}+ 39^{\circ}\).

Answer:

\(78\)