Question

1. label the following statements as true or false: a. m∠3 + m∠5 = 180 b. m∠2 + m∠6 = 180 c. m∠8 = m∠1

Explanation:

Step1: Recall angle - pair relationships

In a parallel - lines and transversals scenario, if two lines are parallel and cut by a transversal, same - side interior angles are supplementary (sum to 180°) and corresponding angles are equal.

Step2: Analyze statement a

If we assume two parallel lines cut by a transversal, ∠3 and ∠5 are same - side interior angles. So, \(m\angle3 + m\angle5=180^{\circ}\) is True when the lines are parallel.

Step3: Analyze statement b

∠2 and ∠6 are corresponding angles. Corresponding angles are equal, not supplementary. So, \(m\angle2 + m\angle6 = 180^{\circ}\) is False.

Step4: Analyze statement c

∠8 and ∠1 are corresponding angles. If the lines are parallel, corresponding angles are equal. So, \(m\angle8=m\angle1\) is True.

Answer:

a. True
b. False
c. True