https://file.aiquickdraw.com/mathbot/file/1729986420422idtkhyih.jpg

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

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

2. **Objective:**
   - Find \( m\angle FHG \).

### Step-by-Step Solution

1. **Identify Key Points and Relationships:**
   - We see that \( \angle CIH \) and \( \angle BGD \) are provided directly.
   - The line \( CI \) and \( HI \) intersect at point \( H \), forming an angle \( CIH = 100^\circ \).
   - The line \( BG \) and \( GD \) intersect at point \( G \), forming an angle \( BGD = 37^\circ \).

2. **Utilize Geometry Properties:**
   - Since \( \angle CIH = 100^\circ \), \( \angle FHG \) might be part of a linear pair or related to angles around points \( H \) or \( G \).
   - We need to explore the configuration of other angles around point \( H \) and point \( G \).

3. **Calculate Based on Linear Pair or Supplementary Angles:**
   - At point \( G \), \( \angle BGD = 37^\circ \), and since \( \angle FHG \) forms a line with \( BG \) and extends towards \( F \), \( \angle FHG \) will be a linear pair with \( \angle BGD \).
   - Therefore:
     \[
     m\angle FHG = 180^\circ - m\angle BGD
     \]
     \[
     m\angle FHG = 180^\circ - 37^\circ = 143^\circ
     \]

### Conclusion
The measure of \( \angle FHG \) is \( 143^\circ \).

Would you like further details, or do you have any additional questions? 

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### Related Questions

1. What are linear pairs and how do they relate to supplementary angles?
2. How can we use vertical angles to find missing angles in such configurations?
3. Can \( m\angle CIH \) affect other unknown angles in this diagram?
4. What are other methods to solve for angles in intersecting line diagrams?
5. How do parallel line angle properties apply if any lines in the diagram were parallel?

### Tip
When dealing with intersecting lines, remember that angles across from each other (vertical angles) are always equal, and angles on a straight line (linear pairs) add up to 180 degrees.

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

Explore how to find the measure of angle FHG given that m∠CIH = 100° and m∠BGD = 37° in a geometry diagram. This problem involves angle relationships and the linear pair theorem, suitable for Grades 8-10.

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