Question

intro to adjacent angles, vertical angles, & linear pair...
identify the linear pair(s) that include ∠7.
∠6 ∠7 ∠8, ∠7
are ∠5 and ∠3 linear pairs?
are ∠6 and ∠8 vertical angles?
are ∠2 and ∠5 vertical angles?

Explanation:

Step1: Recall the definition of linear pair

A linear pair of angles is a pair of adjacent angles that form a straight line. The sum of angles in a linear pair is \(180^{\circ}\), and angles that sum to \(180^{\circ}\) are called supplementary.

Step2: Analyze each option

• Sum is \(180^{\circ}\): By the definition of linear pair, this is correct.
• Are Supplementary: Since supplementary angles sum to \(180^{\circ}\) and linear - pair angles sum to \(180^{\circ}\), this is correct.
• Form a Line: A linear pair forms a straight line (by definition), so this is correct.
• Do NOT have a common vertex: A linear pair has a common vertex (as they are adjacent angles), so this is incorrect.

Answer:

A. Sum is \(180^{\circ}\), B. Are Supplementary, C. Form a Line