2016 AMC 12B Problems/Problem 4

Problem

The ratio of the measures of two acute angles is $5:4$ , 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?

$\textbf{(A)}\ 75\qquad\textbf{(B)}\ 90\qquad\textbf{(C)}\ 135\qquad\textbf{(D)}\ 150\qquad\textbf{(E)}\ 270$

Solution

We can set up equations to find each angle. The larger angle will be represented as $x$ and the larger angle will we represented as $y$ . We can get the equations

$4x=5y$

and

$2\times(90-x)=90-y$

since the larger the original angle, the smaller the complement. We then find that $x=75$ and $y=60$ , there sum is $\boxed{\textbf{(C)}\ 135}$

2016 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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All AMC 12 Problems and Solutions

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2016 AMC 12B Problems/Problem 4

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