Maths Olympiad Prep

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 6060^{\circ} and 130130^{\circ}. What can be said about its other angles?

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

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Official solution

Δ\Delta The angles at the lateral side of the trapezoid add up to 180180^{\circ} (as interior alternate angles). Therefore, there are also angles 18060=120180^{\circ}-60^{\circ}=120^{\circ} and 180130=50180^{\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.