Question

quadrilateral wxyz is a strict trapezoid with a pair of opposite supplementary angles. is wxyz an isosceles trapezoid?
yes
no

Explanation:

A strict trapezoid has exactly one pair of parallel sides. In a trapezoid, consecutive angles between the bases are supplementary. If a trapezoid has a pair of opposite supplementary angles, let's recall the properties of isosceles trapezoids: in an isosceles trapezoid, base angles are equal, and opposite angles are supplementary (since consecutive angles between bases are supplementary, and base angles are equal, so opposite angles sum to 180°). Also, a trapezoid with a pair of opposite supplementary angles (and one pair of parallel sides) must have the non - parallel sides equal (by using angle - side - angle or other congruence criteria, or by the property that if in a trapezoid opposite angles are supplementary, it implies the trapezoid is isosceles). So, if quadrilateral \(WXYZ\) is a strict trapezoid (one pair of parallel sides) and has a pair of opposite supplementary angles, it must be an isosceles trapezoid.

Answer:

Yes