Question 557292: The measure of an angle is 2x+16 and the measure of its complement is x-7. How do you find the value of x? Found 2 solutions by mananth, bucky:Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! angle = 2x+16 degrees
complement = x-7
sum of angles = 90 deg
2x+16+x-7 = 90
3x+9=90
3x=90-9
3x=81
/3
x=27
You can put this solution on YOUR website! The definition of "complementary angles" is "two angles whose measures add up to 90 degrees." Therefore, to solve this problem, you can just add the measures of the two angles and set that sum equal to 90.
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So you can say:
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(2x + 16) + (x - 7) = 90
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The parentheses were just used to show the two angles. They can be removed as follows:
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2x + 16 + x - 7 = 90
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Combine the two terms containing x by adding 2x + x to get 3x. This makes the equation:
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3x + 16 - 7 = 90
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Combine the two constants on the left side by subtracting 7 from 16 to get +9. This reduces the equation to:
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3x + 9 = 90
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Get rid of the +9 on the left side by subtracting 9 from both sides:
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3x = 81
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Solve for x by dividing both sides by 3 and you have the answer:
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x = 81/3 = 27
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The answer is x equals 27 degrees.
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This means that the measure of one of the angles is 2x + 16 which is 54 + 16 = 70 degrees. The measure of the second angle is x - 7 which is 27 - 7 = 20 degrees. And the sum of the measures of two of the angles is 70 + 20 = 90 degrees.
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I hope this helps you to understand this problem.
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