Lines a and b are parallel. What is the measure of ∠5 if ∠1 measures 116°? A) 32° B) 58° C) 64° D) 116°

Note: As you missed to add the diagram, so I have attached a reference diagram below to explain you the concept.

The measure of ∠5 is 64°.

In other words: m∠5 = 64°.

Step-by-step explanation:

Considering the attache diagram below.

m∠1 = 116°

As we know that when parallel lines are cut by a transversal, corresponding angles will be congruent.

From the figure angle ∠1 and angle ∠6 are congruent.

i.e.

m∠1 = m∠6 = 116°

As m∠6 are m∠5 are supplementary angles as they both add up to 180° angle. The reason is that m∠5 and m∠6 are linear pairs, on a straight line, so they are supplementary.

m∠5 + m∠6 = 180°

m∠5 + 116° = 180°           ∵ m∠6 = 116°

m∠5 = 180° - 116°

m∠5 = 64°

Therefore, the measure of ∠5 is 64°.

In other words: m∠5 = 64°.

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step-by-step explanation:

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step-by-step explanation: