Question

In the following figure (AB) (CD) Suppose that m∡3=52°. What is the measure of ∡5? Explain your reasoning I NEED FULL DETAIL

Answer 1

m∠5 = 52°

Explanation:

Alternate Interior Angles Theorem

If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.

As line AB is parallel to line CD, angles 3 and 5 are alternate interior angles, and are therefore congruent according to the Alternate Interior Angles Theorem.

⇒ m∠5 = m∠3 = 52°

Answer 2

• m∠5 = 52°

Explanation:

Given

• AB ║ CD and
• m∠3 = 52°

From the diagram we see that ∠3 and ∠5 are alternate interior angles, since located on opposite sides of the transversal.

As per definition, alternate interior angles are congruent and therefore:

• ∠5 ≅ ∠3, so
• m∠5 = m∠3 = 52°