SOLUTION: The measure of an angle is 20 degrees more than twice its complement. Find the measure of the smaller angle.

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Question 622545: The measure of an angle is 20 degrees more than twice its complement. Find the measure of the smaller angle.
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--
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Let m be the measure of the angle.
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Since the sum of the measures of an angle and its complement is 90 degrees, we can write the measure of the complement as 90-m.
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We know that the measure of the angle is 20 degrees more than twice the complement.
[the measure of the angle] = [twice the measure of the complement] + [20 degrees more]
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In algebra we write,
m=2%2A%2890-m%29%2B20
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Simplify and solve for m.
m=180-2m%2B20
m=-2m%2B200
3m=200
m=66%262%2F3
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Since the angle measures 66%262%2F3 degrees, its complement it 23%261%2F3 degrees.
So, the smaller angle has a measure of 23%261%2F3 degrees.
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It's always a good idea to check your answer against the information in the original problem.
Twice the complement is 2%2A%2823%261%2F3%29=46%262%2F3 degrees. In addition, 66%262%2F3 degrees is 20 more degrees than 46%262%2F3 degrees.
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That's it! Feel free to email me if you have questions about this.
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Ms.Figgy
math.in.the.vortex@gmail.com