15. name a set of each type of angle pairs.
alternate interior angles ______ same side exterior angles ______
alternate exterior angles ______ corresponding angles ______
same side interior angles ______ vertical angles ______

Question

15. name a set of each type of angle pairs.
alternate interior angles ______  same side exterior angles ______
alternate exterior angles ______  corresponding angles ______
same side interior angles ______  vertical angles ______

Accepted Answer

To solve this, we identify a set (pair) for each angle type using the properties of parallel lines cut by a transversal:

### Alternate Interior Angles
Let two parallel lines $ l $ and $ m $ be cut by a transversal $ t $. Alternate interior angles are non - adjacent, on opposite sides of the transversal, and inside the two lines. For example, $ \angle 3 $ and $ \angle 6 $ (if we label the angles formed in the standard way with $ l\parallel m $ and $ t $ as transversal). A common set is $ \boldsymbol{\angle 3} $ and $ \boldsymbol{\angle 6} $ (in the standard angle - labeling for parallel lines and transversal).

### Same Side Exterior Angles
Same - side exterior angles are on the same side of the transversal and outside the two parallel lines. For example, if we have parallel lines $ l $ and $ m $ cut by transversal $ t $, $ \angle 1 $ and $ \angle 8 $ (using standard angle numbering) form a set of same - side exterior angles. So a set is $ \boldsymbol{\angle 1} $ and $ \boldsymbol{\angle 8} $.

### Alternate Exterior Angles
Alternate exterior angles are on opposite sides of the transversal and outside the two parallel lines. For parallel lines $ l $ and $ m $ cut by transversal $ t $, $ \angle 1 $ and $ \angle 8 $ are same - side exterior, while $ \angle 1 $ and $ \angle 7 $ (wait, no, correct alternate exterior angles: $ \angle 1 $ and $ \angle 8 $ is same - side, alternate exterior would be $ \angle 1 $ and $ \angle 7 $? No, let's recall: when $ l\parallel m $ and $ t $ is transversal, alternate exterior angles are $ \angle 1 $ and $ \angle 8 $? No, I made a mistake. Let's use the correct definition. If the two parallel lines are $ l $ (top) and $ m $ (bottom), and transversal $ t $ crosses them, the angles above $ l $ and below $ m $ are exterior. Alternate exterior angles are $ \angle 1 $ (top - left exterior) and $ \angle 8 $ (bottom - right exterior)? No, better to take a concrete example. Let $ l\parallel m $, transversal $ t $. Angles: $ \angle 1 $ (top - left, exterior), $ \angle 2 $ (top - right, exterior), $ \angle 3 $ (top - left, interior), $ \angle 4 $ (top - right, interior), $ \angle 5 $ (bottom - left, interior), $ \angle 6 $ (bottom - right, interior), $ \angle 7 $ (bottom - left, exterior), $ \angle 8 $ (bottom - right, exterior). Then alternate exterior angles are $ \angle 1 $ and $ \angle 8 $? No, $ \angle 1 $ and $ \angle 7 $ are same - side exterior, $ \angle 2 $ and $ \angle 8 $ are same - side exterior. Alternate exterior angles: $ \angle 1 $ and $ \angle 8 $ are not alternate, $ \angle 2 $ and $ \angle 7 $ are alternate exterior. So a set of alternate exterior angles is $ \boldsymbol{\angle 2} $ and $ \boldsymbol{\angle 7} $.

### Corresponding Angles
Corresponding angles are in the same relative position at each intersection. For example, $ \angle 1 $ (top - left, exterior) and $ \angle 5 $ (bottom - left, interior) are not corresponding. Wait, $ \angle 1 $ (top - left, exterior) and $ \angle 5 $ (bottom - left, interior) – no, corresponding angles: $ \angle 1 $ and $ \angle 5 $ (same position: left - most, top and bottom), $ \angle 2 $ and $ \angle 6 $, $ \angle 3 $ and $ \angle 7 $, $ \angle 4 $ and $ \angle 8 $. So a set of corresponding angles is $ \boldsymbol{\angle 1} $ and $ \boldsymbol{\angle 5} $.

### Same Side Interior Angles
Same - side interior angles are on the same side of the transversal and inside the two parallel lines. For example, $ \angle 3 $ and $ \angle 5 $ (using the angle numbering above). So a set is $ \boldsymbol{\angle 3} $ and $ \boldsymbol{\angle 5} $.

### Vertical Angles
Vertical angles are opposite each other when two lines intersect. If two lines intersect at a point, forming angles $ \angle A $, $ \angle B $, $ \angle C $, $ \angle D $ (in order), then $ \angle A $ and $ \angle C $ are vertical, $ \angle B $ and $ \angle D $ are vertical. For example, if two lines intersect and we have $ \angle 1 $ and $ \angle 3 $ (opposite each other), then $ \boldsymbol{\angle 1} $ and $ \boldsymbol{\angle 3} $ form a set of vertical angles.

(Note: The specific angle labels can vary based on the diagram, but the above are standard examples for each angle - pair type.)

### Answers (Examples for each type):
- Alternate Interior Angles: $ \angle 3 $ and $ \angle 6 $
- Same Side Exterior Angles: $ \angle 1 $ and $ \angle 8 $
- Alternate Exterior Angles: $ \angle 2 $ and $ \angle 7 $
- Corresponding Angles: $ \angle 1 $ and $ \angle 5 $
- Same Side Interior Angles: $ \angle 3 $ and $ \angle 5 $
- Vertical Angles: $ \angle 1 $ and $ \angle 3 $

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QUESTION IMAGE

Question

Explanation:

Alternate Interior Angles

Same Side Exterior Angles

Alternate Exterior Angles

Corresponding Angles

Same Side Interior Angles

Answer: