Question

1. which diagram(s) show adjacent angles? 26. which diagram(s) show vertical angles? 27. which diagram(s) show complementary angles? 28. which diagram(s) show supplementary angles? 29. which diagram(s) show a linear pair? use the diagrams below to answer 25 - 29.

Explanation:

Step1: Recall angle - pair definitions

Adjacent angles share a common side and a common vertex. Complementary angles add up to 90°. Supplementary angles add up to 180°. Vertical angles are opposite each other when two lines intersect. A linear - pair is a pair of adjacent angles that are supplementary.

Step2: Analyze each diagram for adjacent angles

In diagram A, the two angles share a common side and vertex, so they are adjacent. In diagram B, ∠1 and ∠2 share a common side and vertex, so they are adjacent. In diagram C, the two angles share a common side and vertex, so they are adjacent. In diagram D, the two angles share a common side and vertex, so they are adjacent. In diagram E, the two angles share a common side and vertex, so they are adjacent. In diagram F, the two angles share a common side and vertex, so they are adjacent.

Step3: Analyze for complementary angles

In diagram A, \(61^{\circ}+29^{\circ}=90^{\circ}\), so they are complementary.

Step4: Analyze for supplementary angles

In diagram E, \(45^{\circ}+135^{\circ}=180^{\circ}\), so they are supplementary.

Step5: Analyze for vertical angles

In diagram B, ∠1 and ∠2 are vertical angles as they are opposite each other when two lines intersect.

Step6: Analyze for linear - pair

In diagram E, the two adjacent angles \(45^{\circ}\) and \(135^{\circ}\) form a linear - pair since they are adjacent and supplementary.

Answer:

1. A, B, C, D, E, F
2. B
3. A
4. E
5. E