https://file.aiquickdraw.com/mathbot/file/1725468786301l579nc55.jpg

To solve for the measure of angle \( \angle FGH \), let's analyze the given information in the image.

### Step-by-Step Solution:

1. **Identify the Angles:**
   - The image shows three rays originating from point \( G \).
   - We are given that:
     - \( \angle EGH = 35^\circ \) (the pink angle adjacent to \( \angle FGH \)).
     - We need to find \( m \angle FGH \).

2. **Understand the Relationships:**
   - Since \( EF \) and \( HI \) appear to form a straight line (a linear pair with \( \angle EGH + \angle FGH = 180^\circ \)), we know that the sum of the angles along a straight line is \( 180^\circ \).

3. **Calculate \( m \angle FGH \):**
   \[
   \angle FGH = 180^\circ - \angle EGH
   \]
   Substituting the given value:
   \[
   \angle FGH = 180^\circ - 35^\circ = 145^\circ
   \]

### Answer:
The measure of \( m \angle FGH \) is **145 degrees**.

Would you like further clarification on this, or do you have any other questions?

### Related Questions to Explore:
1. What is the sum of all angles around a point?
2. How to determine if two angles are supplementary?
3. What are linear pairs and their properties?
4. How can we calculate unknown angles when given a diagram?
5. What is the importance of knowing angle relationships in geometry?

**Tip:** Remember that angles forming a straight line always add up to \( 180^\circ \). This property is essential in solving many geometry problems!

Discover how to solve for m∠FGH in a geometry problem involving linear pairs. This detailed solution covers key geometric concepts such as angle relationships and the Linear Pair Theorem. Perfect for students in Grades 7-9.

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