Interior Angles of a Right-Angled Trapezoid
publish date: 2026/05/16 01:15:5.894516 UTC
A trapezoid PQRS has parallel top and bottom bases PQ and SR. Side PS is perpendicular to both bases, creating internal right angles at vertices P and S. If the measure of angle R is discovered to be \(118^\circ\), find the degree measurement of angle Q.
Correct Answer
Explanation
In any trapezoid, the two angles that share a non-parallel leg side are consecutive interior angles between parallel lines, making them supplementary (\(180^\circ\)).
Leg segment QR connects parallel bases PQ and SR. This rules that \(\angle Q\) and \(\angle R\) must sum to exactly \(180^\circ\):
\[ m\angle Q + m\angle R = 180^\circ \]
\[ m\angle Q + 118^\circ = 180^\circ \]
\[ m\angle Q = 180^\circ - 118^\circ = 62^\circ \]
Reference
Mathematics for college students