Question

what is ( mangle fhg )?
( mangle fhg=square^{circ} )
learn about angle bisectors!

Explanation:

Step1: Use the Angle Bisector Theorem

Since \(FG = FI\) (marked as equal) and \(HG\perp FG\), \(HI\perp FI\), by the converse of the Angle Bisector Theorem, \(FH\) is the angle bisector of \(\angle GHI\).

Step2: Calculate \(\angle FHG\)

We know that \(\angle GHI\) is composed of \(\angle FHG\) and \(\angle FHI\). Since \(FH\) is the angle bisector, \(\angle FHG=\angle FHI\). Given \(\angle FHI = 36^{\circ}\), then \(m\angle FHG=36^{\circ}\)

Answer:

\(36\)