In the given figure, `l||m` and a transversal t cuts them. If ∠7=`80^(@)`, find the measure of each of the remaining marked angles.

Explanation

To solve the problem step by step, we will use the properties of angles formed by parallel lines and a transversal.

### Step-by-Step Solution:

1. **Identify Given Information:**
- We are given that \( l \parallel m \) (lines l and m are parallel).
- A transversal \( t \) intersects these lines.
- The measure of angle 7 is given as \( 80^\circ \).

2. **Find Angle 5:**
- Angle 5 is vertically opposite to angle 7.
- By the property of vertically opposite angles, we have:
\[ \text{Angle 5} = \text{Angle 7} = 80^\circ \]

3. **Find Angle 6:**
- Angles 5 and 6 are on a straight line (they form a linear pair).
- The sum of angles on a straight line is \( 180^\circ \).
- Therefore, we can write:
\[ \text{Angle 6} + \text{Angle 5} = 180^\circ \]
- Substituting the value of angle 5:
\[ \text{Angle 6} + 80^\circ = 180^\circ \]
- Solving for angle 6:
\[ \text{Angle 6} = 180^\circ - 80^\circ = 100^\circ \]

4. **Find Angle 8:**
- Angle 8 is vertically opposite to angle 6.
- By the property of vertically opposite angles, we have:
\[ \text{Angle 8} = \text{Angle 6} = 100^\circ \]

5. **Find Angle 1:**
- Angle 1 is corresponding to angle 5.
- By the property of corresponding angles, we have:
\[ \text{Angle 1} = \text{Angle 5} = 80^\circ \]

6. **Find Angle 3:**
- Angle 3 is vertically opposite to angle 1.
- By the property of vertically opposite angles, we have:
\[ \text{Angle 3} = \text{Angle 1} = 80^\circ \]

7. **Find Angle 2:**
- Angle 2 is corresponding to angle 6.
- By the property of corresponding angles, we have:
\[ \text{Angle 2} = \text{Angle 6} = 100^\circ \]

8. **Find Angle 4:**
- Angle 4 is vertically opposite to angle 2.
- By the property of vertically opposite angles, we have:
\[ \text{Angle 4} = \text{Angle 2} = 100^\circ \]

### Summary of Angles:
- Angle 1 = \( 80^\circ \)
- Angle 2 = \( 100^\circ \)
- Angle 3 = \( 80^\circ \)
- Angle 4 = \( 100^\circ \)
- Angle 5 = \( 80^\circ \)
- Angle 6 = \( 100^\circ \)
- Angle 7 = \( 80^\circ \)
- Angle 8 = \( 100^\circ \)