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a + d – c – 90

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a + d – c – 90 [#permalink] New post 15 Sep 2017, 07:43
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Question Stats:

42% (02:35) correct 57% (02:29) wrong based on 14 sessions



Attachment:
triangle.jpg
triangle.jpg [ 28.43 KiB | Viewed 1134 times ]


Quantity A
Quantity B
a + d – c – 90
90 – e – b – f


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 + d – c – 90 [#permalink] New post 16 Sep 2017, 08:29
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My idea is to make the two columns as similar as possible. So exploiting the parallelism of AC and FD, I found that b°=c°, e°=180°-b°-d° and that f = 180°-(180°-b)-a =b-a. Substituting these equalities in column B, I get that it is equal to 90°+a°-c°+d°. Thus, the answer is C.
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Re: a + d – c – 90 [#permalink] New post 22 Sep 2017, 15:47
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Carcass wrote:
Attachment:
triangle.jpg


Quantity A
Quantity B
a + d – c – 90
90 – e – b – f




Given:
Quantity A: a + d – c – 90
Quantity B: 90 – e – b – f


First recognize that, since AC||FD, ∠b = ∠c
So, we can replace b with c to get:
Quantity A: a + d – c – 90
Quantity B: 90 – e – c – f

Add c to both quantities to get:
Quantity A: a + d – 90
Quantity B: 90 – e – f

Now add 90 to both quantities to get:
Quantity A: a + d
Quantity B: 180 – e – f

Now add e and f to both quantities to get:
Quantity A: a + d + e + f
Quantity B: 180

Finally, notice that, since AC||FD, ∠d = ∠BCD
So, replace ∠d with ∠BCD to get:
Quantity A: a + ∠BCD + e + f
Quantity B: 180

At this point, we should recognize that Quantity A represents the sum of all three angles of ∆ACE
As such, Quantity A MUST equal 180

Answer:
[Reveal] Spoiler:
C


Cheers,
Brent
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Re: a + d – c – 90   [#permalink] 22 Sep 2017, 15:47
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