+305
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.
+9675 In fact, you have more information than enough to determine the angle.
Note that ∠ZXW,∠XWZ,∠XZW are the 3 interior angles of △WXZ, so they should add up to 180∘.
Then,
90∘+60∘+∠XZW=180∘
∠XZW=30∘
The information about Y can be arbitrary, it does not affect the answer.
This particular condition on Y (i.e., ∠XYZ=120∘) just makes the diagram easy to draw because it is an isosceles trapezoid, i.e., WX = YZ.
