Question

1. (4pt) consider this figure that shows two parallel lines cut by a transversal. determine whether each angle listed in the table has the same measurement as < 1, is supplementary to <1, adjacent to < 1 or corresponding <1.

Explanation:

Step1: Analyze ∠2

∠1 and ∠2 are adjacent angles. They form a linear - pair. So, ∠1 + ∠2=180°, ∠2 is supplementary to ∠1.

Step2: Analyze ∠4

∠1 and ∠4 are vertical angles. Vertical angles are equal. So, ∠4 has the same measurement as ∠1.

Step3: Analyze ∠5

∠1 and ∠5 are corresponding angles. Since lines \(s\) and \(t\) are parallel and \(r\) is a transversal, corresponding angles are equal. So, ∠5 has the same measurement as ∠1.

Step4: Analyze ∠7

∠1 and ∠7: ∠1 = ∠4 (vertical angles), ∠4+∠5 = 180° (linear - pair), ∠5 = ∠7 (vertical angles). So, ∠1+∠7 = 180°, ∠7 is supplementary to ∠1.

Answer:

Angle	Same as ∠1	Supplementary to ∠1	Neither
∠4	✔
∠5	✔
∠7		✔