Question

fh bisects ∠efg. find the indicated angle measures. m∠efh = 63 °. find m∠gfh and m∠efg.

Explanation:

Step1: Recall angle - bisector property

A ray that bisects an angle divides the angle into two congruent angles. Since $FH$ bisects $\angle EFG$, then $\angle EFH\cong\angle GFH$.

Step2: Find $m\angle GFH$

Given $m\angle EFH = 63^{\circ}$, and $\angle EFH\cong\angle GFH$, so $m\angle GFH=m\angle EFH = 63^{\circ}$.

Step3: Find $m\angle EFG$

Since $\angle EFG=\angle EFH+\angle GFH$ and $\angle EFH = \angle GFH=63^{\circ}$, then $m\angle EFG=m\angle EFH + m\angle GFH=63^{\circ}+63^{\circ}=126^{\circ}$.

Answer:

$m\angle GFH = 63^{\circ}$
$m\angle EFG = 126^{\circ}$