https://file.aiquickdraw.com/mathbot/file/1728506784949uycvkaxe.jpg

Let's analyze the image and solve for the unknown angle measures based on the given information.

1. **m∠5**: 
   - Angle ∠5 is given as \( 63^\circ \) (directly labeled in the diagram).

2. **m∠1 and m∠4 (Vertically Opposite Angles)**:
   - Vertically opposite angles are always equal. Thus, 
     \[
     m∠1 = m∠5 = 63^\circ \quad \text{and} \quad m∠4 = 63^\circ.
     \]

3. **m∠2 and m∠3 (Linear Pair/ Supplementary Angles)**:
   - Angles ∠2 and ∠3 are supplementary with the adjacent angles.
   - For ∠2: \( 31^\circ + m∠2 = 180^\circ \), so:
     \[
     m∠2 = 180^\circ - 31^\circ = 149^\circ.
     \]
   - For ∠3: \( 49^\circ + m∠3 = 180^\circ \), so:
     \[
     m∠3 = 180^\circ - 49^\circ = 131^\circ.
     \]

### Final Answers:
- \( m∠1 = 63^\circ \)
- \( m∠2 = 149^\circ \)
- \( m∠3 = 131^\circ \)
- \( m∠4 = 63^\circ \)
- \( m∠5 = 63^\circ \)

Would you like further clarification on any of these solutions?

Here are some follow-up questions for deeper understanding:
1. What is the relationship between supplementary angles?
2. How are vertically opposite angles identified in a diagram?
3. What makes linear pairs of angles supplementary?
4. How do you calculate an unknown angle in a triangle when one angle is known?
5. Why do the angles around a point always add up to 360°?

**Tip**: When dealing with angles around a point or in a line, remember that angles in a straight line sum to 180°, and angles around a point sum to 360°.

Determine the measures of angles 1, 2, 3, 4, and 5 using the given angle diagram, including the known angles of 31°, 49°, and 63°.

This problem requires solving for angles 1, 2, 3, 4, and 5 using concepts like vertically opposite and supplementary angles. Known angles include 31°, 49°, and 63°, suitable for students in Grades 7-9.

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