volume_mute
Sum of Interior Angles of a Quadrilateral
publish date: 2026/05/16 01:15:6.129041 UTC
In a structural scale model, a flat structural support bracket is shaped as a generic trapezoid. Three of its interior angles are accurately measured to be \(112^\circ\), \(68^\circ\), and \(135^\circ\). What must be the measure of the final, fourth interior angle?
Answer = (1)
Correct Answer
(1) 45
Explanation
A trapezoid is fundamentally a four-sided polygon (quadrilateral). The interior angles of any Euclidean quadrilateral always sum up to exactly \(360^\circ\).
Let \(x\) be the unknown fourth angle measure:
\[ 112^\circ + 68^\circ + 135^\circ + x = 360^\circ \]
\[ 315^\circ + x = 360^\circ \]
\[ x = 360^\circ - 315^\circ = 45^\circ \]
Reference
Mathematics for college students