Question

fill in the sentence below with the description that most specifically applies to the quadrilateral below.
answer attempt 1 out of 2
the quadrilateral is most specifically a ~ , because

• both pairs of sides are parallel
• all angles measure $90^\circ$
• no sides are congruent or parallel
• it is equilateral and it is equiangular

Explanation:

First, verify side congruence: the side lengths are 106, 175, 103, 79, so no sides are equal. Next, check parallel sides: for a quadrilateral, consecutive interior angles should be supplementary (sum to $180^\circ$) if sides are parallel. The consecutive angle pairs are $45^\circ+153^\circ=198^\circ
eq180^\circ$, $153^\circ+86^\circ=239^\circ
eq180^\circ$, $86^\circ+76^\circ=162^\circ
eq180^\circ$, $76^\circ+45^\circ=121^\circ
eq180^\circ$, so no sides are parallel. Eliminate other options: angles are not all $90^\circ$, sides are not parallel, and it is not equilateral/equiangular.

Answer:

The quadrilateral is most specifically a scalene quadrilateral, because no sides are congruent or parallel