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Which of the following must be true of the angles marke

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Which of the following must be true of the angles marke [#permalink] New post 01 Jan 2019, 15:10
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82% (00:55) correct 17% (00:52) wrong based on 29 sessions
Image

Which of the following must be true of the angles marked in the figure above?

I. a + b = d + e
II. b + e = c + f
III. a + c + e = b + d + f

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
[Reveal] Spoiler: OA

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Re: Which of the following must be true of the angles marke [#permalink] New post 01 Jan 2019, 18:55
Expert's post
GreenlightTestPrep wrote:
Image

Which of the following must be true of the angles marked in the figure above?

I. a + b = d + e
II. b + e = c + f
III. a + c + e = b + d + f

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III



property - Opposite angles are equal
So, a=d, b=e and c=f.

I. a + b = d + e
Since a=d and b=e, their sum a+b=d+e
Hence true..

II. b + e = c + f
we can write this as b+b=c+c....b=c
But we do not know the relation between b and c..
Hence need not be true

III. a + c + e = b + d + f
Since a=d, b=e and c=f, both sides are equal.

I and III are true..

C
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Some useful Theory.
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2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
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4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

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Re: Which of the following must be true of the angles marke [#permalink] New post 02 Jan 2019, 06:26
Expert's post
GreenlightTestPrep wrote:
Image

Which of the following must be true of the angles marked in the figure above?

I. a + b = d + e
II. b + e = c + f
III. a + c + e = b + d + f

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III


Since opposite angles are equal, let's first denote pairs of equal angles with the same symbols.
Image

Now, we'll check the statements...

I. a + b = d + e
We can rewrite this as: (red dot) + (blue star) = (blue star) + (red dot)
Definitely TRUE (always!)
Since statement I is true, we can ELIMINATE answer choice D

II. b + e = c + f
We can rewrite this as: (blue star) + (blue star) = (green square) + (green square)
This need not be true
Since statement II is false, we can ELIMINATE answer choices B and E

III. a + c + e = b + d + f
We can rewrite this as: (red dot) + (green square) + (blue star) = (blue star) + (red dot) + (green square)
Definitely TRUE (always!)
Since statement III is true, we can ELIMINATE answer choice A

Answer: C

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Re: Which of the following must be true of the angles marke   [#permalink] 02 Jan 2019, 06:26
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