Question

identifying types of angles: check all relationships between ∠1 and ∠2.

1. adjacent
2. vertical
3. complementary
4. supplementary
5. linear pair

Explanation:

Step1: Recall angle - relationship definitions

Adjacent angles share a common side and a common vertex. Vertical angles are non - adjacent angles formed by two intersecting lines and are congruent. Complementary angles add up to 90 degrees. Supplementary angles add up to 180 degrees. A linear pair is a pair of adjacent angles that are supplementary.

Step2: Analyze each case

Case 1:

• Adjacent: Share a common side and vertex.
• Vertical: Not adjacent, formed by intersecting lines.
• Complementary: Sum to 90°.
• Supplementary: Sum to 180°.
• Linear Pair: Adjacent and supplementary.

Case 2:

• If the angle between them is 90°, they are complementary and adjacent.

Case 3:

• Check for each relationship as above.

Case 4:

• If they are part of a larger angle and share a side, they are adjacent.

Case 5:

• Similar to previous cases, check all relationships.

Case 6:

• Analyze based on the definitions of angle relationships.

Answer:

We need specific angle - measure and position information for each of the six cases shown in the figure to accurately check all the relationships (adjacent, vertical, complementary, supplementary, linear pair) between ∠1 and ∠2 for each case. Without angle - measure and more detailed position information for each pair of angles in the six sub - figures, we cannot provide a definite answer for each checkbox.