for each, state the angle relationship.
1. angle $ \angle 1 $ and $ \angle 8 $ are...
2. angle $ \angle 3 $ and $ \angle 1 $ are...
3. angle $ \angle 1 $ and $ \angle 5 $ are...
4. angle $ \angle 4 $ and $ \angle 8 $ are...
5. angle $ \angle 2 $ and $ \angle 6 $ are...
6. angle $ \angle 4 $ and $ \angle 5 $ are...
7. angle $ \angle 2 $ and $ \angle 7 $ are...
8. angle $ \angle 3 $ and $ \angle 6 $ are...
9. angle $ \angle 4 $ and $ \angle 7 $ are...
10. angle $ \angle 3 $ and $ \angle 2 $ are...
11. angle $ \angle 7 $ and $ \angle 6 $ are...
12. angle $ \angle 5 $ and $ \angle 7 $ are...
13. angle $ \angle 1 $ and $ \angle 6 $ are...
14. angle $ \angle 6 $ and $ \angle 3 $ are...
15. angle $ \angle 5 $ and $ \angle 6 $ are...
16. angle $ \angle 2 $ and $ \angle 4 $ are...
17. angle $ \angle 7 $ and $ \angle 3 $ are...
18. angle $ \angle 5 $ and $ \angle 2 $ are...

Question

Accepted Answer

# Explanation:
## Step1: Recall angle - relationship definitions
- **Alternate exterior angles**: Non - adjacent exterior angles that lie on opposite sides of the transversal.
- **Corresponding angles**: Angles that are in the same relative position with respect to the parallel lines and the transversal.
- **Linear pair**: Adjacent angles that form a straight line ($\angle a+\angle b = 180^{\circ}$).
- **Vertical angles**: Opposite angles formed by the intersection of two lines ($\angle a=\angle b$).
- **Alternate interior angles**: Non - adjacent interior angles that lie on opposite sides of the transversal.
- **Consecutive interior angles**: Interior angles that lie on the same side of the transversal ($\angle a+\angle b=180^{\circ}$ if the lines are parallel).

## Step2: Analyze each pair
1. **For $\angle1$ and $\angle8$**:
   - They are non - adjacent exterior angles and lie on opposite sides of the transversal. So, they are alternate exterior angles.
2. **For $\angle3$ and $\angle1$**:
   - There is no specific standard angle - relationship (not corresponding, alternate interior/exterior, vertical, linear pair or consecutive interior).
3. **For $\angle1$ and $\angle5$**:
   - They are adjacent angles that form a straight line. So, they are a linear pair.
4. **For $\angle4$ and $\angle8$**:
   - They are opposite angles formed by the intersection of two lines. So, they are vertical angles.
5. **For $\angle2$ and $\angle6$**:
   - They are adjacent angles that form a straight line. So, they are a linear pair.
6. **For $\angle4$ and $\angle5$**:
   - They are non - adjacent interior angles and lie on opposite sides of the transversal. So, they are alternate interior angles.
7. **For $\angle2$ and $\angle7$**:
   - They are non - adjacent angles. There is no specific standard angle - relationship (not corresponding, alternate interior/exterior, vertical, linear pair or consecutive interior).
8. **For $\angle3$ and $\angle6$**:
   - They are non - adjacent interior angles and lie on opposite sides of the transversal. So, they are alternate interior angles.
9. **For $\angle4$ and $\angle7$**:
   - They are adjacent angles that form a straight line. So, they are a linear pair.
10. **For $\angle3$ and $\angle2$**:
   - They are non - adjacent interior angles and lie on the same side of the transversal. So, they are consecutive interior angles.
11. **For $\angle7$ and $\angle6$**:
   - They are adjacent angles that form a straight line. So, they are a linear pair.
12. **For $\angle5$ and $\angle7$**:
   - They are in the same relative position with respect to the parallel lines and the transversal. So, they are corresponding angles.
13. **For $\angle1$ and $\angle6$**:
   - There is no specific standard angle - relationship (not corresponding, alternate interior/exterior, vertical, linear pair or consecutive interior).
14. **For $\angle6$ and $\angle3$**:
   - They are non - adjacent interior angles and lie on opposite sides of the transversal. So, they are alternate interior angles.
15. **For $\angle5$ and $\angle6$**:
   - They are adjacent angles that form a straight line. So, they are a linear pair.
16. **For $\angle2$ and $\angle4$**:
   - There is no specific standard angle - relationship (not corresponding, alternate interior/exterior, vertical, linear pair or consecutive interior).
17. **For $\angle7$ and $\angle3$**:
   - They are opposite angles formed by the intersection of two lines. So, they are vertical angles.
18. **For $\angle5$ and $\angle2$**:
   - They are non - adjacent exterior angles and lie on opposite sides of the transversal. So, they are alternate exterior angles.

# Answer:
1. Alternate exterior angles
2. No specific standard relationship
3. Linear pair
4. Vertical angles
5. Linear pair
6. Alternate interior angles
7. No specific standard relationship
8. Alternate interior angles
9. Linear pair
10. Consecutive interior angles
11. Linear pair
12. Corresponding angles
13. No specific standard relationship
14. Alternate interior angles
15. Linear pair
16. No specific standard relationship
17. Vertical angles
18. Alternate exterior angles

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QUESTION IMAGE

Question

Explanation:

Step1: Recall angle - relationship definitions

Step2: Analyze each pair

Answer: