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

Expert's post

GreenlightTestPrep wrote:

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.

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