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2002 AMC 12A Problem 4

Problem 4 of 25EasierAlgebraGeometry

Find the degree measure of an angle whose complement is 25%25\% of its supplement.

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Solution

Let the angle be x.x. Then 90−x=14(180−x),90 - x = \dfrac14(180 - x), so 360−4x=180−x.360 - 4x = 180 - x. This gives 3x=180,3x = 180, so x=60.x = 60. Thus, the correct answer is B.

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Concepts: angle sum · linear equation

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.