
∠EFG and ∠GFH are a linear pair, m∠EFG = 2n + 21, and m∠GFH = 4n + 15. Find n.
What are m∠EFG and m∠GFH? (Write an equation to solve)

Since ∠EFG and ∠GFH are a **linear pair**, they are supplementary, meaning their measures add up to \(180^\circ\). 

We are given:
- \( m\angle EFG = 2n + 21 \)
- \( m\angle GFH = 4n + 15 \)

To solve for \(n\), we use the fact that their sum is 180 degrees:

\[
(2n + 21) + (4n + 15) = 180
\]

### Step 1: Combine like terms
\[
6n + 36 = 180
\]

### Step 2: Subtract 36 from both sides
\[
6n = 144
\]

### Step 3: Solve for \(n\)
\[
n = \frac{144}{6} = 24
\]

Now that we have \(n = 24\), we can find the measures of the angles:

### \(m\angle EFG\)
\[
m\angle EFG = 2n + 21 = 2(24) + 21 = 48 + 21 = 69^\circ
\]

### \(m\angle GFH\)
\[
m\angle GFH = 4n + 15 = 4(24) + 15 = 96 + 15 = 111^\circ
\]

Thus, the measures of the angles are:
- \( m\angle EFG = 69^\circ \)
- \( m\angle GFH = 111^\circ \)

Would you like further details or explanations?

Here are 5 related questions for further practice:
1. If two angles form a linear pair, what is their sum?
2. What is the value of \(n\) if \(m\angle EFG = 3n + 10\) and \(m\angle GFH = 5n + 20\)?
3. What are supplementary angles?
4. What are complementary angles, and how are they different from supplementary angles?
5. If the sum of two angles is 90 degrees, what are those angles called?

**Tip:** In a linear pair, always remember that the sum of the angles is 180°, as they lie on a straight line.

∠EFG and ∠GFH are a linear pair, m∠EFG = 2n + 21, and m∠GFH = 4n + 15. Find n. What are m∠EFG and m∠GFH? (Write an equation to solve)

Learn how to solve for n in the linear pair problem involving ∠EFG and ∠GFH, where m∠EFG = 2n + 21 and m∠GFH = 4n + 15. This detailed solution explains how to apply the Linear Pair Theorem to find the measures of the angles. Suitable for students in Grades 8-10.

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