Question

1. use the diagram. tell whether the angles are vertical angles, a linear pair, or neither.

a.) ∠1 and ∠3
b.) ∠6 and ∠7
c.) ∠2 and ∠3
d.) ∠5 and ∠8
e.) ∠4 and ∠9
f.) ∠4 and ∠5

Explanation:

Step1: Recall definitions

Vertical angles are opposite angles formed by two intersecting lines. A linear - pair of angles are adjacent angles that form a straight line.

Step2: Analyze ∠1 and ∠3

They are adjacent and form a straight line. So, they are a linear pair.

Step3: Analyze ∠6 and ∠7

They are adjacent and form a straight line. So, they are a linear pair.

Step4: Analyze ∠2 and ∠3

They are adjacent but do not form a straight line. They are neither vertical angles nor a linear pair.

Step5: Analyze ∠5 and ∠8

They are vertical angles as they are opposite angles formed by two intersecting lines.

Step6: Analyze ∠4 and ∠9

They are vertical angles as they are opposite angles formed by two intersecting lines.

Step7: Analyze ∠4 and ∠5

They are adjacent and form a straight line. So, they are a linear pair.

Answer:

a. Linear pair
b. Linear pair
c. Neither
d. Vertical angles
e. Vertical angles
f. Linear pair