Question

lines a and b are parallel. what is the measure of ∠5 if ∠1 measures 116°? a 32° b 58° c 64° d 116°

Explanation:

Step1: Find the measure of ∠3

∠1 and ∠3 are vertical angles. Vertical angles are equal. So, ∠3 = ∠1 = 116°.

Step2: Find the measure of ∠5

∠3 and ∠5 are supplementary angles (because lines \(a\) and \(b\) are parallel and they are same - side interior angles). The sum of supplementary angles is \(180^{\circ}\). So, ∠5=180° - ∠3. Substitute ∠3 = 116° into the formula: ∠5 = 180° - 116° = 64°.

Answer:

C. 64°