https://file.aiquickdraw.com/mathbot/file/1726068111656maeceync.jpg

Looking at the diagram and based on the angles provided, I will help you determine the measures of the angles labeled from \( m \angle 1 \) to \( m \angle 7 \). 

### Step-by-step breakdown:
1. **\( m \angle 1 \):**
   \( m \angle 1 \) is supplementary to \( 80^\circ \) because they form a linear pair. Hence, 
   \[
   m \angle 1 = 180^\circ - 80^\circ = 100^\circ
   \]

2. **\( m \angle 2 \):**
   \( m \angle 2 \) and \( 115^\circ \) are vertically opposite angles, so:
   \[
   m \angle 2 = 115^\circ
   \]

3. **\( m \angle 3 \):**
   \( m \angle 3 \) forms a linear pair with \( m \angle 2 \), so:
   \[
   m \angle 3 = 180^\circ - 115^\circ = 65^\circ
   \]

4. **\( m \angle 4 \):**
   \( m \angle 4 \) is vertically opposite to \( 65^\circ \) (from \( m \angle 3 \)), so:
   \[
   m \angle 4 = 65^\circ
   \]

5. **\( m \angle 5 \):**
   This is a supplementary angle to \( 115^\circ \) and shares a straight line, so:
   \[
   m \angle 5 = 180^\circ - 115^\circ = 65^\circ
   \]

6. **\( m \angle 6 \):**
   \( m \angle 6 \) is part of a triangle. The sum of angles in a triangle is \( 180^\circ \). In the triangle with \( 61^\circ \), \( 90^\circ \) (right angle), and \( m \angle 6 \), we have:
   \[
   m \angle 6 = 180^\circ - 61^\circ - 90^\circ = 29^\circ
   \]

7. **\( m \angle 7 \):**
   \( m \angle 7 \) is a right angle, so:
   \[
   m \angle 7 = 90^\circ
   \]

### Final Angle Measures:
- \( m \angle 1 = 100^\circ \)
- \( m \angle 2 = 115^\circ \)
- \( m \angle 3 = 65^\circ \)
- \( m \angle 4 = 65^\circ \)
- \( m \angle 5 = 65^\circ \)
- \( m \angle 6 = 29^\circ \)
- \( m \angle 7 = 90^\circ \)

Would you like further details or explanations on any specific part?

### Related Questions:
1. How are vertically opposite angles formed and calculated?
2. Why do linear pairs of angles always add up to \( 180^\circ \)?
3. Can you explain why the angles of a triangle always sum to \( 180^\circ \)?
4. How do you calculate unknown angles in a right triangle?
5. How can angle relationships help solve complex geometric problems?

**Tip**: When dealing with a triangle, always remember that the sum of all interior angles is \( 180^\circ \).

Determine the measures of the angles labeled from m∠1 to m∠7 based on the provided diagram.

Learn how to calculate the angle measures in a geometric diagram using the properties of supplementary angles and vertical angles. This problem covers geometry concepts related to linear pairs and the sum of angles in a triangle, suitable for students in Grades 8-10.

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