identifying angle pairs use the figure at the right.
13) are $\angle 5$ and $\angle 6$ a linear pair?
14) are $\angle 5$ and $\angle 9$ a linear pair?
15) are $\angle 5$ and $\angle 8$ a linear pair?
16) are $\angle 5$ and $\angle 8$ vertical angles?
17) are $\angle 5$ and $\angle 7$ vertical angles?

Question

Accepted Answer

To solve these problems, we need to recall the definitions of a linear pair and vertical angles:

- **Linear Pair**: Two adjacent angles that form a straight line (their non - common sides are opposite rays, and their sum is $180^{\circ}$).
- **Vertical Angles**: Two non - adjacent angles formed by two intersecting lines (they are opposite each other and have equal measures).

### Problem 13: Are $\angle5$ and $\angle6$ a linear pair?
## Step 1: Check adjacency and straight line formation
$\angle5$ and $\angle6$ are adjacent (they share a common side) and their non - common sides form a straight line (since they lie on a straight line in the figure). So, they satisfy the definition of a linear pair.
# Answer: Yes

### Problem 14: Are $\angle5$ and $\angle9$ a linear pair?
## Step 1: Check adjacency and straight line formation
$\angle5$ and $\angle9$ are adjacent (they share a common side) and their non - common sides form a straight line (as seen from the figure). So, they form a linear pair.
# Answer: Yes

### Problem 15: Are $\angle5$ and $\angle8$ a linear pair?
## Step 1: Check adjacency and straight line formation
$\angle5$ and $\angle8$ are not adjacent (they do not share a common side in a way that forms a linear pair) and their non - common sides do not form a straight line. So, they do not satisfy the linear pair definition.
# Answer: No

### Problem 16: Are $\angle5$ and $\angle8$ vertical angles?
## Step 1: Check the formation of vertical angles
Vertical angles are formed by two intersecting lines. $\angle5$ and $\angle8$ are not formed by two intersecting lines in the required way (they are not opposite each other). So, they are not vertical angles.
# Answer: No

### Problem 17: Are $\angle5$ and $\angle7$ vertical angles?
## Step 1: Check the formation of vertical angles
$\angle5$ and $\angle7$ are not opposite each other when two lines intersect. Vertical angles are opposite each other. So, they do not satisfy the vertical angles definition.
# Answer: No

### Final Answers (for each problem):
13. Yes
14. Yes
15. No
16. No
17. No

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QUESTION IMAGE

Question

Explanation:

Problem 13: Are \(\angle5\) and \(\angle6\) a linear pair?

Step 1: Check adjacency and straight line formation

Answer:

Problem 14: Are \(\angle5\) and \(\angle9\) a linear pair?

Step 1: Check adjacency and straight line formation