Question

1. higher order thinking 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.

Explanation:

Step1: Recall angle - pair properties

In a trapezoid, assume the two parallel sides are cut by non - parallel sides (transversals). $\angle1$ and $\angle3$ are same - side interior angles, and $\angle2$ and $\angle4$ are also same - side interior angles.

Step2: Apply same - side interior angle theorem

When two parallel lines are cut by a transversal, same - side interior angles are supplementary. So, $\angle1+\angle3 = 180^{\circ}$ and $\angle2+\angle4=180^{\circ}$.

Answer:

$\angle1+\angle3 = 180^{\circ}$ and $\angle2+\angle4 = 180^{\circ}$ because they are pairs of same - side interior angles formed by parallel lines and transversals in the trapezoid.