Difference between revisions of "2016 AMC 10B Problems/Problem 7"
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Revision as of 13:05, 21 February 2016
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?
Solution
We can set up a system of equations where and
are the two acute angles. WLOG, assume that
in order for the complement of
to be greater than the complement of
. Therefore,
and
. Solving for
in the first equation and substituting into the second equation yields
Substituting this
value back into the first equation yields
, leaving
equal to
.
See Also
2016 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
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