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Which is greater a+b-c or zero
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28 Dec 2018, 11:18
28 Dec 2018, 11:18
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Quantity A |
Quantity B |
a+b-c |
0 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Joined: 21 Nov 2018
Posts: 24
Given Kudos: 0
GRE 1: Q170 V170
Re: Which is greater a+b-c or zero
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28 Dec 2018, 18:58
28 Dec 2018, 18:58
1
In the case of a triangle with one of the sides extended we have what is called an external supplementary angle (in this problem this angle is C degrees). It is "External" because it is not one of the three angles that makes up the triangle. "Supplementary" because it sits on a straight line and together with the adjacent interior angle it adds to 180.
Let's call the final angle inside the triangle D degrees. So inside the triangle we have angles of measures A degrees B degrees and D degrees. The external supplementary angle is C degrees. From here on I will just call them angles A B D and C.
With the supplementary angle rule we know that any two angles that make a straight line are equal to 180 degrees. So C + D = 180.
But it is also true that the angles that make up a triangle equal 180 degrees. So A + B + D = 180.
Since they each equal 180 we can set these equations equal to each other so that A + B + D = C + D. Subtract D from each side and you have A + B = C
The rule that takes you directly to "A + B = C" is as follows, "The measure of an external supplementary angle is equal to the sum of the two internal non-adjacent angles."
Clearly if A + B = C then quantity A equals zero.
Let's call the final angle inside the triangle D degrees. So inside the triangle we have angles of measures A degrees B degrees and D degrees. The external supplementary angle is C degrees. From here on I will just call them angles A B D and C.
With the supplementary angle rule we know that any two angles that make a straight line are equal to 180 degrees. So C + D = 180.
But it is also true that the angles that make up a triangle equal 180 degrees. So A + B + D = 180.
Since they each equal 180 we can set these equations equal to each other so that A + B + D = C + D. Subtract D from each side and you have A + B = C
The rule that takes you directly to "A + B = C" is as follows, "The measure of an external supplementary angle is equal to the sum of the two internal non-adjacent angles."
Clearly if A + B = C then quantity A equals zero.
