Difference between revisions of "2016 AMC 12B Problems/Problem 4"

Revision as of 16:07, 27 August 2018

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

By: dragonfly

We set up equations to find each angle. The larger angle will be represented as $x$ and the smaller angle will be represented as $y$ , in degrees. This implies that

$4x=5y$

and

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

since the larger the original angle, the smaller the complement.

We then find that $x=75$ and $y=60$ , and their 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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

@@ Line 8: / Line 8: @@
 By: dragonfly
-We set up equations to find each angle. The larger angle will be represented as <math>x</math> and the larger angle will we represented as <math>y</math>, in degrees. This implies that
+We set up equations to find each angle. The larger angle will be represented as <math>x</math> and the smaller angle will be represented as <math>y</math>, in degrees. This implies that
 <math>4x=5y</math>

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Difference between revisions of "2016 AMC 12B Problems/Problem 4"

Revision as of 16:07, 27 August 2018

Problem

Solution

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