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Question 242791: Find the measure of an angle whose supplement exceeds its complement by 90 degrees
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! Define terms:
x = unknown angle
The complement will be defined in terms of x, so it is 90 - x.
Likewise, the supplement will be in terms of x, to it is 180 - x.
The question's setup tells us the relationship of the complement and supplement.
(180 - x) is 90 degrees greater than the complement (90 - x).
(180 - x) = (90 - x) + 90 OR
(180 - x) - 90 = (90 - x)
Simplifying the equations we have:
90 - x = 90 - x.
That is a tautology.
It seems the supplement of an angle must be 90 degrees greater than the complement of the angle.
To test this theory, let's try a few values of x.
Say, x = 0: (180 - 0) = (90 - 0) + 90. True
Say, x = 89: (180 - 89) = (90 - 89) + 90. True
Say, x = 45: (180 - 45) = (90 - 45) + 90. True
This question appears to ask you to understand the definitions of complement and supplement.
The complement is the angle that, when added to x, totals 90 degrees.
The supplement is the angle that, when added to x, totals 180 degrees.
So the supplement will always be 90 degrees more than the complement.
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