SOLUTION: If two angles are supplementary and congruent,then they are right angles. True or False?

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Question 1032785: If two angles are supplementary and congruent,then they are right angles. True or False?
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
If two angles are supplementary and congruent,then they are right angles. True or False?
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True::
x + y = 180 (supplementary)
x = y (congruent)
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Substitute for x and solve for "y"::
y + y = 180
2y = 180
y = 90 degrees
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Since x = y , x = 90 degrees also.
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Cheers,
Stan H.
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Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Suppose ∠A and ∠B are supplementary and congruent.

Then since they are supplementary,

m∠A + m∠B = 180°

And since they are congruent,

m∠A = m∠B

Substituting equals for equals in m∠A + m∠B = 180°

m∠B + m∠B = 180°

2m∠B = 180°

Divings both sides by 2

m∠B = 90°

So ∠B is a right angle

And since m∠B = m∠A

m∠A = 90°

So ∠B is a right angle

So it's true that they are both right angles.

Edwin
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