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25 Dec 2018, 02:41
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C
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Difficulty:
5%
(low)
Question Stats:
85% (01:03) correct
15%
(01:21)
wrong
based on 165
sessions
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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
Attachment:
2018-12-25_1339.png [ 11.29 KiB | Viewed 16099 times ]
01 Jan 2019, 15:58
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Bunuel
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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01 Jan 2019, 20:34
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Solution
Given:
- • Three straight lines
To find:
- • Which of the given statements are always true?
Approach and Working:
We know that,
- • a + b + c =180, and
• c + d + e = 180
So, a + b + c = c + d + e
- • Implies, a + b = d + e
Now, from the diagram we can say that, a + b + c = f + d + e
- • Implies, c = f
And, we can also say that, a + f + e = b + c + d
- • Since, f = c, we can interchange them.
• Thus, we get, a + c + e = b + f + d
Hence, the correct answer is Option C
Answer: C
