SOLUTION: Angles A and B are complementary angles. If the measure of angle A is 54 degrees less than the measure of angle B, find the measures of the two angles.

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Question 620307: Angles A and B are complementary angles. If the measure of angle A is 54 degrees less than the measure of angle B, find the measures of the two angles.
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--
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Let a be the measure of angle A in degrees.
Let b be the measure of angle B in degrees.
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Since the angles are complementary, their sum is 90 degrees. We can write,
a%2Bb=90
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We know that "the measure of angle A is 54 degrees less than the measure of angle B." In algebra, we can write,
a=b-54
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Now we have a system of equations in two variables. Solve the system to find the measure of each angle. Substitute b-54 for a in the first equation.
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a%2Bb=90
%28b-54%29%2Bb=90
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Simplify by combining like terms.
2b-54=90
2b=90%2B54
2b=144
b=72
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The measure of angle B is 72 degrees. To find the measure of angle A, substitute 72 for b in the first equation.
a%2Bb=90
a%2B72=90
a=90-72
a=18
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The measure of angle A is 18 degrees.
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Now we need to check our answers against the information in the problem.
Yes, angles A and B are complementary because their angle measures add to 90 degrees (18+72=90).
Yes, the measure of angle A is 53 degrees less than the measure of angle B (72-18=54).
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Hope this helps! Feel free to email if you still have questions about this.
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Ms.Figgy
math.in.the.vortex@gmail.com