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.

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) (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,

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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,

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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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Simplify by combining like terms.

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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.

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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

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