Question

lines a and b are parallel. what is the measure of ∠8 if ∠1 measures 110°?
a 35°
b 55°
c 70°
d 110°

Explanation:

Step1: Find the measure of ∠3

∠1 and ∠3 are vertical angles. Vertical angles are equal. So, ∠3 = ∠1 = 110°.

Step2: Find the measure of ∠5

∠3 and ∠5 are same - side interior angles. Since lines a and b are parallel, ∠3+∠5 = 180° (same - side interior angles are supplementary). Then ∠5=180° - ∠3 = 180° - 110° = 70°.

Step3: Find the measure of ∠8

∠5 and ∠8 are vertical angles. Vertical angles are equal. So, ∠8 = ∠5 = 70°.

Answer:

C. 70°