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In the figure, lines l and k are parallel. Which one of the
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17 Mar 2019, 02:21
17 Mar 2019, 02:21
Expert Reply
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Question Stats:
80% (01:24) correct
19% (01:45) wrong based on 21 sessions
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#GREpracticequestion In the figure, lines l and k are parallel.jpg [ 18.37 KiB | Viewed 6408 times ]
In the figure, lines \(l\) and \(k\) are parallel. Which one of the following must be true?
(A) \(a < b\)
(B) \(a ≤ b\)
(C) \(a = b\)
(D) \(a ≥ b\)
(E) \(a > b\)
Re: In the figure, lines l and k are parallel. Which one of the
[#permalink]
20 Mar 2019, 14:28
20 Mar 2019, 14:28
1
Expert Reply
I drew an imaginary line passing through point O and forming two right triangles, as seen in the attached image.
The angles at O must all add up to 180, so:
60 - b + 90 - b + a = 180
Combine like terms:
150 - 2b + a = 180
Add 2b to both sides:
150 + a = 180 + 2b
Subtract 180:
a - 30 = 2b
Okay, now what is this equation telling us? Well, if we start with a and make it smaller by 30, then it will be equal to twice b. We can see, then, that a must be much greater than b, making the answer E, a > b.
The angles at O must all add up to 180, so:
60 - b + 90 - b + a = 180
Combine like terms:
150 - 2b + a = 180
Add 2b to both sides:
150 + a = 180 + 2b
Subtract 180:
a - 30 = 2b
Okay, now what is this equation telling us? Well, if we start with a and make it smaller by 30, then it will be equal to twice b. We can see, then, that a must be much greater than b, making the answer E, a > b.
Attachments
In the figure, lines l and k are parallel. If a is an acut.png [ 14.51 KiB | Viewed 6288 times ]
Re: In the figure, lines l and k are parallel. Which one of the
[#permalink]
14 Aug 2022, 18:09
14 Aug 2022, 18:09
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