Question

using what you know about angle pairs formed by parallel lines and a transversal, how are ∠1, ∠2, ∠3, and ∠4 related in the trapezoid? explain. ∠1 and ∠□ are □ and ∠2 and ∠□ are □ because they are □

Explanation:

Step1: Identify angle - pair types

If the trapezoid has one pair of parallel sides and a transversal (the non - parallel sides can be considered in terms of angle - pair relationships), $\angle1$ and $\angle3$ are same - side interior angles. They are on the same side of the non - parallel side (transversal - like) and between the parallel sides of the trapezoid. $\angle2$ and $\angle4$ are also same - side interior angles for the same reason.

Step2: State the relationship

Same - side interior angles formed by parallel lines and a transversal are supplementary, that is, $\angle1+\angle3 = 180^{\circ}$ and $\angle2+\angle4=180^{\circ}$ if the trapezoid has parallel sides.

Answer:

$\angle1$ and $\angle3$ are same - side interior angles; $\angle2$ and $\angle4$ are same - side interior angles; they are supplementary because they are same - side interior angles formed by parallel lines and a transversal.