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 Post subject: GMAT Geometry
PostPosted: Sat Jul 28, 2012 12:05 pm 
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Joined: Tue Apr 13, 2010 8:48 am
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The complement of an angle is one quarter of the supplement of the angle. What is the measure of the angle?

Solution
Let x be the measure of the angle.
Its complement c is x + c = 90, so x = 90 – c.
Its supplement s is x + s = 180, so x = 180 – s.

The complement is one quarter of the supplement, so c = s/4.

90 – c = 180 – s Subtract 90 and add s to both sides.

sc = 90 Substitute c = s/4.

ss/4 = 90

3s/4 = 90 Multiply both sides by 4/3.

s = 120

x + s = 180, so x = 180 – 120 = 60 so the measure of the angle is 60°.
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Why can't we suppose this:
the complement is quarter of the supplement, so the equation could be: 90 – x = (180 – x)/4 .


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 Post subject: Re: GMAT Geometry
PostPosted: Sat Jul 28, 2012 12:11 pm 
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Joined: Thu Jul 05, 2012 11:55 am
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questioner wrote:
Why can't we suppose this:
the complement is quarter of the supplement, so the equation could be: 90 – x = (180 – x)/4 .
We can. This equation will also work here.


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 Post subject: Re: GMAT Geometry
PostPosted: Mon Jul 30, 2012 1:57 pm 
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Joined: Tue Apr 13, 2010 8:48 am
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Thanks for your reply!


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