2002 AMC 12A Problems/Problem 4

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 $\frac{1}{4} of the supplementary angle. Subtracting the complementary angle from the supplementary angle, we have$ 90^{\circ} $as$ \frac{3}{4}$of the supplementary angle.

Thus the degree measure of the supplementary angle is$ (Error compiling LaTeX. Unknown error_msg)120^{\circ} $, and the degree measure of the desired angle is$ 180^{\circ} - 120^{\circ} = 60^{\circ} $.$

2002 AMC 12A (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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2002 AMC 12A Problems/Problem 4

Contents

Problem

Solution

Solution 1

Solution 2

See Also