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Question 120651: Two congruent angles are supplementary. Find the measure of both angles.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Call the two angles A and B
.
You are told that the two angles are supplementary. That means that when you add the measure
of angle A (call it mA) and the measure of angle B (call it mB) the resulting sum is 180 degrees.
This relationship can be written in equation form as:
.
mA + mB = 180
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You are also told that the two angles are congruent. This means that their measures
are equal. You can write this relationship as the equation:
.
mA = mB
.
From this second equation you can see that wherever you have mA you can substitute mB
in its place because they are equals. So go back to the equation:
.
mA + mB = 180
.
In place of mA substitute mB. This makes the equation become:
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mB + mB = 180
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On the left side you can see that the sum is 2 times mB or 2*mB. Make this simplification
to get:
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2*mB = 180
.
To solve for mB divide both sides of this equation by 2. When you do that division the
equation reduces to:
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mB = 180/2 = 90
.
This tells you that the measure of angle B is 90 degrees, and that means that the measure
of angle A is also equal to 90 degrees because the two angles are congruent.
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Hope this helps you to understand the problem.
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