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Question 545104: The problem is: find the measure of an angle that is half as large as its complement. Help me please!
Answer by lmeeks54(111)   (Show Source):
You can put this solution on YOUR website! This problem is checking to see if you know what complementary angles are. Complementary angles are two angles that add up to a right angle (90 degrees). By the way, you don't need it for this problem, but another useful definition is supplementary angles: two angles that add up to 180 degrees.
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Let a = an acute angle (an acute angle is < 90 degrees)
Let b = its complement (another acute angle)
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We know by their definition that:
a + b = 90
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We are given a is half as large as its complement, b:
b = 2a
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Use substitution and insert the identity for b into the first equation:
a + b = 90
a + 2a = 90
3a = 90
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divide both sides by 3:
a = 30 degrees
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this is the answer to the problem
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to check our work, calculate b:
a + b = 90
30 + b = 90
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subtract 30 from both sides:
b = 60 degrees
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2a = b
2(30) = 60
60 = 60 checks
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cheers,
Lee
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