\( \overrightarrow{F H} \) bisects \( \angle E F G \). Find the indicated angle measures. \( m \angle E F H=63^{\circ} \). Find \( m \angle G F H \) and \( m \angle E F G \). \( m \angle G F H=\square^{\circ} \) \( m \angle E F G=\square^{\circ} \)

To solve the problem, let's analyze the given information step by step. ### Given: 1. **Ray \( \overrightarrow{FH} \)** bisects the angle \( \angle EFG \). This means that \( \overrightarrow{FH} \) divides \( \angle EFG \) into two equal parts. 2. **Measure of \( \angle EFH = 63^\circ \)**. ### Find: 1. **Measure of \( \angle GFH \)** 2. **Measure of \( \angle EFG \)** ### Solution: 1. **Understanding the Angle Bisector:** Since \( \overrightarrow{FH} \) bisects \( \angle EFG \), it divides \( \angle EFG \) into two congruent angles: \[ \angle EFH = \angle GFH \] 2. **Given \( \angle EFH = 63^\circ \):** Therefore, \[ \angle GFH = 63^\circ \] 3. **Calculating \( \angle EFG \):** Since \( \angle EFG \) is the sum of \( \angle EFH \) and \( \angle GFH \): \[ \angle EFG = \angle EFH + \angle GFH = 63^\circ + 63^\circ = 126^\circ \] ### **Final Answers:** - \( m \angle GFH = 63^\circ \) - \( m \angle EFG = 126^\circ \)