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In the figure, lines l and k are parallel. If a is an acut
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17 Mar 2019, 02:24
17 Mar 2019, 02:24
Expert Reply
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Question Stats:
83% (01:36) correct
16% (00:56) wrong based on 6 sessions
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#GREpracticequestion In the figure, lines l and k are parallel.jpg [ 18.37 KiB | Viewed 4266 times ]
In the figure, lines \(l\) and \(k\) are parallel. If a is an acute angle, then which one of the following must be true?
(A) \(b > 10\)
(B) \(b > 15\)
(C) \(b < 20\)
(D) \(b < 30\)
(E) \(b > 45\)
Re: In the figure, lines l and k are parallel. If a is an acut
[#permalink]
20 Mar 2019, 11:24
20 Mar 2019, 11:24
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
Now, if a is acute, less than 90, then (a - 30) must be less than 60. This means that 2b must be less than 60, and hence that b must be less than 30.
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
Now, if a is acute, less than 90, then (a - 30) must be less than 60. This means that 2b must be less than 60, and hence that b must be less than 30.
Attachments
In the figure, lines l and k are parallel. If a is an acut.png [ 14.51 KiB | Viewed 4171 times ]
gmatclubot
Re: In the figure, lines l and k are parallel. If a is an acut [#permalink]
20 Mar 2019, 11:24
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