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The problem states that ∠EFG and ∠GFH form a linear pair. Since the two angles form a linear pair, their sum must equal 180°.

We are given:
- m∠EFG = \( 5n + 16 \)
- m∠GFH = \( 2n + 17 \)

To find the values of these angles, follow these steps:

### Step 1: Set up the equation
Since the sum of the two angles must be 180° (because they form a linear pair), we can write the equation:

\[
(5n + 16) + (2n + 17) = 180
\]

### Step 2: Simplify the equation
Combine like terms:

\[
7n + 33 = 180
\]

### Step 3: Solve for \( n \)
Subtract 33 from both sides:

\[
7n = 147
\]

Now, divide by 7:

\[
n = 21
\]

### Step 4: Substitute \( n = 21 \) back into the expressions for the angles

- For m∠EFG:
\[
m∠EFG = 5n + 16 = 5(21) + 16 = 105 + 16 = 121^\circ
\]

- For m∠GFH:
\[
m∠GFH = 2n + 17 = 2(21) + 17 = 42 + 17 = 59^\circ
\]

Thus, the measures of the angles are:
- m∠EFG = 121°
- m∠GFH = 59°

Would you like a further breakdown of any part of this solution? Here are some related questions you might explore:

1. What happens if the angles do not form a linear pair?
2. How can we verify if two angles form a linear pair geometrically?
3. What is the significance of linear pairs in polygon angle sums?
4. How do we apply linear pair properties to parallel lines?
5. Can we use the same method to solve for angles that sum to 90°?

**Tip:** In problems involving linear pairs, always remember that the sum of the angles equals 180°, which makes solving for variables straightforward once the equation is set up.

∠EFG and ∠GFH form a linear pair. Given m∠EFG = 5n + 16 and m∠GFH = 2n + 17, find the measures of m∠EFG and m∠GFH.

This problem involves finding the angles of a linear pair where m∠EFG = 5n + 16 and m∠GFH = 2n + 17. Learn how to set up the equation and solve for n to find m∠EFG = 121° and m∠GFH = 59°. Suitable for students in Grades 8-10.

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