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We are given that \( \overrightarrow{FH} \) bisects \( \angle EFG \), and that the measure of \( \angle HFG = 18^\circ \). Since \( \overrightarrow{FH} \) bisects \( \angle EFG \), it divides the angle into two equal parts. 

Thus, \( m \angle EFG = 2 \times m \angle HFG \).

Given that \( m \angle HFG = 18^\circ \), we can calculate \( m \angle EFG \) as follows:

\[
m \angle EFG = 2 \times 18^\circ = 36^\circ
\]

Therefore, the measure of \( \angle EFG \) is \( 36^\circ \).

Would you like further details or have any additional questions?

Here are 5 related questions for practice:
1. If \( \overrightarrow{FH} \) bisects \( \angle ABC \) and \( m \angle HBC = 25^\circ \), what is \( m \angle ABC \)?
2. If a bisector divides an angle into two parts, and one part is \( 45^\circ \), what is the full angle?
3. What is the measure of an angle if it is bisected and each resulting angle is \( 30^\circ \)?
4. If an angle is bisected and the measure of one part is \( 22^\circ \), what is the measure of the full angle?
5. Can an angle bisector divide an obtuse angle? Why or why not?

**Tip:** Always remember, an angle bisector divides an angle into two equal parts!

If FH bisects ∠EFG, and if m∠HFG = 18, then find m∠EFG.

Learn how to find the measure of ∠EFG when FH bisects the angle and m∠HFG is given as 18°. This problem covers key geometric concepts, including angle bisectors and the Angle Bisector Theorem. Suitable for students in Grades 6-8.

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