The Algebra of Complements and Supplements

Date: 01/25/99 at 21:59:31
From: Jalaine Rogers
Subject: Help with Geometry in Algebra I  book.

I'm in Algebra I, and the other day we had an integration in Geometry, 
even though we are in Algebra I. I don't grasp the concept of problems 
like this:

The measure of an angle is 34 degrees greater than its complement. 
Find the measure of each angle.

I also don't grasp the concept of these problems:

Find both the complement and the supplement of each angle measure. 

  y degrees 
  p degrees, (p - 10) degrees 
  c degrees, (2c + 1) degrees

Please write back with any suggestions on these problems. Your help is 
greatly appreciated.

Jalaine Rogers

Date: 01/26/99 at 08:59:31
From: Doctor Rick
Subject: Re: Help with Geometry in Algebra I  book.

Hi, Jalaine.

With these problems, you just need to learn how to translate two
geometry concepts into algebra. Then you can forget the geometry and 
do the algebra. (I don't mean you should forget geometry, but you 
don't need it to do the rest of the problem!)

In geometry, it's easiest to show you what the complement and 
supplement of an angle are:

  |     /
  |    /
  | x /        COMPLEMENT
  |  /
  | / 90-x
  |/__________

                   /
                  /
                 /
                /           SUPPLEMENT
        180-x  /  x
  ____________/____________

An angle and its complement add to a right angle. An angle and its
supplement add to a straight angle. Since a right angle is 90 degrees 
and a straight angle is 180 degrees, the measures of the complement 
and supplement are shown in the figure:

  The complement of an angle x degrees is (90 - x) degrees.

  The supplement of an angle x degrees is (180 - x) degrees.

So, for instance,

  The complement of 30 degrees is 90 - 30 = 60 degrees.

  The supplement of 45 degrees is 180 - 45 = 135 degrees.

  The complement of c degrees is (90-c) degrees.

  The supplement of (p + 10) degrees is (180 - (p + 10)) degrees.

I will leave it to you to simplify that last answer. And here is a 
problem similar to your first problem:

The measure of an angle is 12 degrees greater than its supplement. 
Find the angle.

Call the angle x degrees. The supplement of the angle is (180 - x) 
degrees, so the problem translates into math like this:

  x = 12 + (180 - x)

Add x to both sides:

  2x = 192

Divide both sides by 2:

  x = 96

so the measure of the angle is 96 degrees.

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/