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a + b + c vs 180

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GRE Prep Club Legend
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Joined: 07 Jun 2014
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GRE 1: Q167 V156
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a + b + c vs 180 [#permalink] New post 26 Sep 2018, 15:34
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Question Stats:

69% (00:24) correct 30% (00:12) wrong based on 23 sessions
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Quantity A
Quantity B
a + b + c
180


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.
[Reveal] Spoiler: OA

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Re: a + b + c vs 180 [#permalink] New post 27 Sep 2018, 01:58
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the sum of all exterior angles of all polygons is 360 degrees. hence A is greater than B.
OR
LET A,B,C be the interior angles of a,b,c respectively. Hence, a=180-A, b=180-B, c=180-C.
a+b+c= 180-A+180-B+180-C = 180-180-180- (A+B+C) = 540- 180 (USING ANGLE SUM PROPERTY)
a+b+c=360.
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Re: a + b + c vs 180 [#permalink] New post 12 Jan 2019, 09:28
By polygon exterior angle rule Answer C.
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Re: a + b + c vs 180 [#permalink] New post 14 Jan 2019, 06:46
Expert's post
sandy wrote:
Attachment:
Capture.JPG


Quantity A
Quantity B
a + b + c
180



Let's add 3 extra angles
Image

Since angles in a triangle add to 180°, we can write: x + y + z = 180

Since angles on a line add to 180°, we can write the following:
a + z = 180
b + y = 180
c + x = 180

Add the 3 equations to get: (a + z) + (b + y) + (c + x) = 540
Rewrite as: a + b + c + x + y + z = 540

Since x + y + z = 180, we can write: a + b + c + 180 = 540
Subtract 180 from both sides to get: a + b + c = 360

We get:
QUANTITY A: 360
QUANTITY B: 180

Answer: B

Cheers,
Brent
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Re: a + b + c vs 180   [#permalink] 14 Jan 2019, 06:46
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