SOLUTION: what is the measure of an angle whose measure is 1/2 of its complement angle?

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Question 801205: what is the measure of an angle whose measure is 1/2 of its complement angle?
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
what is the measure of an angle whose measure is 1/2 of its complement angle?
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angle:: x
complement: 90-x
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Equation::
x = (1/2)(90-x)
x = 45 - (1/2)x
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(3/2)x = 45
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x = 30 degrees
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Cheers,
Stan H.
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Complementary angles add up to 90°.
let's an angle be alpha and its complement beta
given:
the measure of an angle whose measure is 1%2F2 of its complement angle

alpha=%281%2F2%29beta....eq.1

alpha%2Bbeta=90.....eq.2....substitute alpha from eq.1
%281%2F2%29beta%2Bbeta=90....solve for beta
3beta%2F2=90
3beta=180
beta=180%2F3
beta=60 => alpha=%281%2F2%29beta=60%2F2=30
so, the measure of an angle whose measure is 1%2F2 of its complement angle
is alpha+=30