Problem:
The ratio of the measures of two acute angles is , and the complement of one of these two angles is twice as large as the complement of the other. What is the sum of the degree measures of the two angles?
Answer Choices:
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Solution:
Let and be the measures of the angles, with . Then . Because , it follows that , so . This leads to the system of linear equations and . Solving the system gives . The requested sum is .
The problems on this page are the property of the MAA's American Mathematics Competitions