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

In the following figure AB CD Suppose that m352 What is the measure of 5 Explain your reasoning I NEED FULL DETAIL class=

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mhanifa

Answer:

  • m∠5 = 52°

Step-by-step 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°
semsee45

Answer:

m∠5 = 52°

Step-by-step 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°

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