Track / Stage 4 / 153 of 340 #413 of 1964

Problem 413

AMC 12 late, AIME early

Geometry Difficulty 4.8 Find the answer

315. 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. Spacing, $ signs and \frac vs / are all fine.

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 and solution reproduced as published; topic, difficulty and ordering added by this site.