Let $WXYZ$ be a trapezoid with bases $\overline{XY}$ and $\overline{WZ}$. In this trapezoid, $\angle ZXW = 90^\circ$, $\angle XWZ = 60^\circ$, and $\angle XYZ = 120^\circ$. Find $\angle XZW$, in degrees.

rtsdylifdts Apr 30, 2024

#1**0 **

In fact, you have more information than enough to determine the angle.

Note that \(\angle ZXW, \angle XWZ, \angle XZW\) are the 3 interior angles of \(\triangle WXZ\), so they should add up to \(180^\circ\).

Then,

\(90^\circ + 60^\circ + \angle XZW = 180^\circ\)

\(\angle XZW = 30^\circ\)

The information about Y can be arbitrary, it does not affect the answer.

This particular condition on Y (i.e., \(\angle XYZ = 120^\circ\)) just makes the diagram easy to draw because it is an isosceles trapezoid, i.e., WX = YZ.

MaxWong Apr 30, 2024