Question

in the diagram, which is not drawn to scale, g is the incenter of △def and m∠efd = 76°. find m∠efg.
m∠efg = \\(\square\\)°

Explanation:

Step1: Recall Incenter Property

The incenter of a triangle is the intersection of angle bisectors. So, \( FG \) bisects \( \angle EFD \).

Step2: Calculate \( m\angle EFG \)

Given \( m\angle EFD = 76^\circ \), since \( FG \) bisects \( \angle EFD \), we have \( m\angle EFG=\frac{1}{2}m\angle EFD \).
Substitute \( m\angle EFD = 76^\circ \): \( m\angle EFG=\frac{76^\circ}{2}=38^\circ \).

Answer:

\( 38 \)