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Question 798150: The measures of two complementary angles are (3x + 3)° and (7x + 5)°. What is the measure of the smaller angle?
Answer by lmeeks54(111)   (Show Source):
You can put this solution on YOUR website! Complementary angles are angles that sum to 90 deg. So, to solve this problem, we need to add the two expressions for the two angles together and set them = 90 degrees:
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(3x + 3) + (7x + 5) = 90
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simplify this by getting all the x terms on one side of the equal sign and all the constants on the other side. Then we can solve for x:
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3x + 7x + 3 + 5 = 90
10x + 8 = 90
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subtract 8 from both sides:
10x + 8 - 8 = 90 - 8
10x = 82
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divide both sides by 10:
10x = 82
x = 8.2
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check our work by going back to the original equation and substituting 8.2 for x in both equations. If we add these two terms together and they = 90 degrees, then we know we did it correctly. Recall, the problem is to determine the value for the smaller angle.
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3x + 3 = ?
7x + 5 = ?
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3(8.2) + 3 = 27.6 deg
7(8.2) + 5 = 62.4 deg
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27.6 + 62.4 = 90
solution checks
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the value for x = 8.2 deg AND, the value for the smaller angle = 27.6 deg
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I hope this helps.
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