https://file.aiquickdraw.com/mathbot/file/1729986270876hnfyxhg4.jpg

To solve for \( m \angle FHG \) in this diagram, let's analyze the given information:

1. **Given Information**:
   - \( m \angle CIH = 100^\circ \)
   - \( m \angle BGD = 37^\circ \)

2. **Observations**:
   - The lines intersect at points \( G \) and \( H \).
   - Since \( \angle CIH \) and \( \angle BGD \) are given, we can apply angle properties related to intersecting lines, such as linear pairs and vertical angles.

3. **Angle Calculation**:
   - We note that \( \angle FHG \) is vertically opposite \( \angle BGD \). In geometry, vertically opposite angles are equal.
   - Therefore, \( m \angle FHG = m \angle BGD = 37^\circ \).

So, the measure of \( \angle FHG \) is:
\[
m \angle FHG = 37^\circ
\]

Would you like further clarification on any step or more details on intersecting line properties?

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**Related Questions**:
1. What are vertically opposite angles, and why are they equal?
2. How can linear pair angles help solve angle relationships?
3. What role does the intersecting line property play in finding unknown angles?
4. Can we use any other approach to verify \( m \angle FHG = 37^\circ \)?
5. How would we proceed if additional angle measures were needed?

**Tip**: In intersecting line problems, look for vertically opposite angles and linear pairs to simplify calculations.

In the diagram below, m∠CIH = 100° and m∠BGD = 37°. Find m∠FHG.

Solve for the angle m∠FHG in the given geometry problem, where m∠CIH = 100° and m∠BGD = 37°. Learn about vertically opposite angles and intersecting line properties with a step-by-step solution. Suitable for students in Grades 8-10.

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