Question

fg bisects ∠agd and m∠agf = 80°. find m∠cge.

Explanation:

Step1: Use the angle - bisector definition

Since \( \overline{FG} \) bisects \( \angle AGD \), then \( \angle AGF=\angle FGD = 80^{\circ} \).

Step2: Calculate \( \angle AGC \)

We know that \( \angle AGC+\angle AGF+\angle FGD = 180^{\circ} \) (a straight - line angle). Substituting \( \angle AGF=\angle FGD = 80^{\circ} \), we get \( \angle AGC=180^{\circ}-80^{\circ}-80^{\circ}=20^{\circ} \).

Step3: Use the vertical - angles theorem

Vertical angles are equal. \( \angle CGE \) and \( \angle AGC \) are vertical angles.

Answer:

\( 20^{\circ} \)