Question

in the diagram below, fg bisects ∠agd and m∠agd = 152°. find m∠egd.

Explanation:

Step1: Recall angle - bisector property

Since $\overline{FG}$ bisects $\angle AGD$, then $\angle AGF=\angle FGD=\frac{1}{2}\angle AGD$. Given $\angle AGD = 152^{\circ}$, so $\angle FGD=\frac{152^{\circ}}{2}=76^{\circ}$.

Step2: Use linear - pair property

$\angle EGD$ and $\angle AGE$ form a linear - pair. Also, $\angle AGE$ and $\angle FGD$ are vertical angles, so $\angle AGE=\angle FGD = 76^{\circ}$. Since $\angle EGD+\angle AGE = 180^{\circ}$ (linear - pair of angles), then $\angle EGD=180^{\circ}-\angle AGE$.

Step3: Calculate $\angle EGD$

Substitute $\angle AGE = 76^{\circ}$ into the formula $\angle EGD=180^{\circ}-\angle AGE$. We get $\angle EGD=180 - 76=104^{\circ}$.

Answer:

$104^{\circ}$