Finding a Consecutive Interior Angle
publish date: 2026/05/16 01:15:5.644148 UTC
In the trapezoid ABCD shown below, side AB is strictly parallel to side DC (\(AB \parallel DC\)). Given that the interior base angle D measures \(73^\circ\), calculate the exact degree measure of interior angle A.
Correct Answer
Explanation
When two parallel lines are cut by a transversal line, the interior angles on the same side of the transversal line are consecutive interior angles and are always supplementary (their sum is \(180^\circ\)).
Here, bases AB and DC are parallel, and the leg side AD functions as the transversal intersecting them. Therefore, \(\angle A\) and \(\angle D\) are supplementary:
\[ m\angle A + m\angle D = 180^\circ \]
\[ x + 73^\circ = 180^\circ \]
\[ x = 180^\circ - 73^\circ = 107^\circ \]
Reference
Mathematics for college students