2002 AMC 12A Problems/Problem 4

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Problem

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

$\mathrm{(A) \ 48 } \qquad \mathrm{(B) \ 60 } \qquad \mathrm{(C) \ 75 } \qquad \mathrm{(D) \ 120 } \qquad \mathrm{(E) \ 150 }$


Solution

Solution 1

We can create an equation for the question, $4(90-x)=(180-x)$

$360-4x=180-x$

$3x=180$

After simplifying, we get $x=60 \Rightarrow \mathrm {(B)}$

Solution 2

Given that the complementary angle is $\frac{1}{4}$ of the supplementary angle, subtracting the complimentary angle from the supplement angle we have 90^{\circ}

See Also

2002 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
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All AMC 12 Problems and Solutions

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