Track / Stage 4 / 177 of 340 #437 of 1964

Problem 437

AMC 12 late, AIME early

Geometry Difficulty 4.8 Find the answer

Two of the angles of a trapezoid are $60^{\circ}$ and $130^{\circ}$ . What can be said about its other angles?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

$\Delta$ The angles at the lateral side of the trapezoid add up to $180^{\circ}$ (as interior alternate angles). Therefore, there are also angles $180^{\circ}-60^{\circ}=120^{\circ}$ and $180^{\circ}-130^{\circ}=50^{\circ}$ in the trapezoid. Thus, all four angles have been found. $\triangleleft$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.