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Which of the following must be true of the angles marke
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01 Jan 2019, 15:10
01 Jan 2019, 15:10
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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
Re: Which of the following must be true of the angles marke
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01 Jan 2019, 18:55
01 Jan 2019, 18:55
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Expert Reply
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
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
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Which of the following must be true of the angles marke
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02 Jan 2019, 06:26
02 Jan 2019, 06:26
1
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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