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555-605 (Medium)|   Geometry|      
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Bunuel
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In the figure, lines l and k are parallel. If a is an acute angle, the Updated on: 22 Jul 2019, 05:46
Originally posted by Bunuel on 18 Mar 2019, 00:03.
Last edited by Sajjad1994 on 22 Jul 2019, 05:46, edited 1 time in total.
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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) \(b > 45\)

Source: Nova GMAT
Difficulty Level: 550

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In the figure, lines l and k are parallel. If a is an acute angle, the Updated on: 20 Mar 2019, 10:13
Originally posted by Archit3110 on 18 Mar 2019, 01:27.
Last edited by Archit3110 on 20 Mar 2019, 10:13, edited 2 times in total.
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Bunuel


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) \(b > 45\)


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solution attached
AjjayKannan
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In the figure, lines l and k are parallel. If a is an acute angle, the 20 Mar 2019, 09:15
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an explanation for the answer, please. Option E seems to be the right one
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In the figure, lines l and k are parallel. If a is an acute angle, the Updated on: 20 Mar 2019, 09:33
Originally posted by anshkool4u on 20 Mar 2019, 09:25.
Last edited by anshkool4u on 20 Mar 2019, 09:33, edited 1 time in total.
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Consider another line m parallel to line k and l,passing through angle b,dividing the angle into angle X and angle a-x.
Now,between angle m and l,angle b+30=angle X
Thus,b+30=X

Between angle k and m,angle b=angle a-x

Thus,angle a=X+a-x= b+30+b=2b+30

Given angle a is acute.
Thus,2b+30<90
b<30.
Hence b.

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In the figure, lines l and k are parallel. If a is an acute angle, the 20 Mar 2019, 09:29
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Consider another line m parallel to line k and l,passing through angle b,dividing the angle into angle X and angle a-x.
Now,between angle m and l,angle b+30=angle X
Thus,b+30=X

Between angle k and m,angle b=angle a-x

Thus,angle a=X+a-x= b+30+b=2b+30

Given angle a is obtuse.
Thus,2b+30<90
b<30.
Hence b.

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Angle a is acute not obtuse
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In the figure, lines l and k are parallel. If a is an acute angle, the 20 Mar 2019, 09:33
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Sorry for the typing mistake.
But I hope,u must have got the clear intent from the solution

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In the figure, lines l and k are parallel. If a is an acute angle, the Updated on: 20 Mar 2019, 10:17
Originally posted by AjjayKannan on 20 Mar 2019, 09:46.
Last edited by AjjayKannan on 20 Mar 2019, 10:17, edited 1 time in total.
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if b+30 is alternate angle and by sum of all angles in a triangle is 180 logic.

[m]B+30 + B + 180 - a = 180[/m]

which is [m]B = [fraction](a-30)/2[/fraction][/m]


When a is acute angle, B will always be equal and below 30 degrees.


Anything wrong in this?
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In the figure, lines l and k are parallel. If a is an acute angle, the 20 Mar 2019, 10:10
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Nothing wrong in this solution.
The only mistake is in the last line,B=(a-30)/2.
For any value of a between 0-89,b will be less than 30 degree.

Ex. When a=89,b=29.5
When a=30,b=0

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In the figure, lines l and k are parallel. If a is an acute angle, the 08 Sep 2023, 22:13
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