Question

1.6 linear pairs & vertical angles homework page 50 & 51 (14,16,20,22,24,26,28,32,34,37 - 42) for questions 14 & 16, use the diagram. 14. identify all the linear pairs that include ∠7. ∠6 ∠7, ∠8 16. are ∠2 and ∠5 vertical angles? explain your reasoning.

Explanation:

Step1: Recall linear - pair definition

A linear pair of angles is a pair of adjacent angles whose non - common sides are opposite rays and the sum of the angles in a linear pair is 180 degrees.

Step2: Identify linear pairs with ∠7

Looking at the diagram, the linear pairs that include ∠7 are ∠6 and ∠7 (since they are adjacent and their non - common sides form a straight line) and ∠7 and ∠8 (for the same reason).

Step3: Recall vertical - angles definition

Vertical angles are two non - adjacent angles formed by two intersecting lines.

Step4: Check if ∠2 and ∠5 are vertical angles

∠2 and ∠5 are not vertical angles because vertical angles are formed by two intersecting lines. ∠2 and ∠5 do not share the same vertex of intersection of two lines in a way that satisfies the vertical - angles definition.

Answer:

1. The linear pairs that include ∠7 are ∠6 and ∠7, ∠7 and ∠8.
2. No, ∠2 and ∠5 are not vertical angles because they are not formed by two intersecting lines in the way required for vertical angles (they do not share the appropriate vertex of intersection).