Question

what is ( mangle fhi )?
( mangle fhi=square^{circ} )

Explanation:

Step1: Prove triangles congruence

In right - angled triangles \( \triangle FIH\) and \( \triangle FGH\), \(FH = FH\) (common side), \(FI=FG = 32\). By the Hypotenuse - Leg (HL) congruence criterion for right - angled triangles, \( \triangle FIH\cong\triangle FGH\).

Step2: Use congruent triangles property

Since \( \triangle FIH\cong\triangle FGH\), then \( \angle FHI=\angle FHG\).

Step3: Calculate \(m\angle FHI\)

We know that \( \angle IHG = 90^{\circ}\) (because \( \angle FIG = 90^{\circ}\) and the sum of angles around a point in the non - overlapping case for the right - angled parts). Given \( \angle FHG=39^{\circ}\), and \(m\angle FHI = m\angle FHG\) (from congruent triangles).

Answer:

\(39\)