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Question 100634: if angles supplement the same angle then?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The angles have equal measures ... or you can say that the angles are congruent.
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Suppose angles A and B are supplementary. By the definition of "supplementary" the measusres
of these two angles add to 180 degrees. So we can write the equation:
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A + B = 180
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in which A represents the measure of angle A and B represents the measure of angle B.
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Now let's suppose that angle C is also supplementary to angle B. By the definition of
supplementary the measures of these two angles add to 180 degrees. This time we can write
the equation as:
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C + B = 180
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in which C represents the measure of angle C and B again represents the measure of angle B.
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Look at the two equations that we have. The right sides of these two equations are equal
because both right sides are 180 degrees. That means that their left sides must also be
equal. Setting their left sides equal results in the equation:
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A + B = C + B
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If you subtract B from both sides of this equation you are left with:
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A = C
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This tells you that if A and C are both supplementary to B, then A equals C which means
that the measures of angles A and C are equal and the angles are congruent.
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Hope this helps you to understand the problem a little better.
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