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In the figure provided, you are given that \( m \angle 1 = 48^\circ \), and you need to find the measures of \( m \angle 2 \), \( m \angle 3 \), and \( m \angle 4 \).

### Step-by-Step Solution:

1. **Identify angle relationships**:
   - \( \angle 1 \) and \( \angle 3 \) are **vertical angles**, meaning they are congruent. So:
     \[
     m \angle 3 = m \angle 1 = 48^\circ
     \]
   
   - \( \angle 2 \) and \( \angle 1 \) are **supplementary angles** (since they form a straight line), meaning their measures add up to \( 180^\circ \). So:
     \[
     m \angle 2 + m \angle 1 = 180^\circ
     \]
     Substituting \( m \angle 1 = 48^\circ \):
     \[
     m \angle 2 + 48^\circ = 180^\circ \quad \Rightarrow \quad m \angle 2 = 180^\circ - 48^\circ = 132^\circ
     \]
   
   - Similarly, \( \angle 2 \) and \( \angle 4 \) are **vertical angles**, meaning they are congruent. So:
     \[
     m \angle 4 = m \angle 2 = 132^\circ
     \]

### Final Answers:
- \( m \angle 2 = 132^\circ \)
- \( m \angle 3 = 48^\circ \)
- \( m \angle 4 = 132^\circ \)

Would you like more details or have any questions?

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### Relative Questions:
1. What is the relationship between vertical angles?
2. How can you identify supplementary angles in a diagram?
3. Can you explain why the sum of supplementary angles is always \(180^\circ\)?
4. How do you know when two angles are congruent?
5. How would the results change if \( m \angle 1 \) were different?

**Tip**: Vertical angles are always congruent, while adjacent angles on a straight line are always supplementary.

In the figure below, m∠1 = 48°. Find m∠2, m∠3, and m∠4.

Learn how to find the measures of m∠2, m∠3, and m∠4 given that m∠1 = 48°. This problem demonstrates the use of vertical and supplementary angle relationships. Suitable for Grade 7-9 students.

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