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655-705 (Hard)|   Geometry|      
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fskilnik
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In the figure shown, all angles are measured in degrees. What is the v 07 Mar 2019, 06:47
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

59% (02:17) correct 41% (01:50) wrong based on 34 sessions

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GMATH practice exercise (Quant Class 1)



In the figure shown, all angles are measured in degrees. What is the value of k?

(A) 18
(B) 20
(C) 22
(D) 25
(E) 27
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B
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thyagi
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GMAT 1: 650 Q49 V30
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In the figure shown, all angles are measured in degrees. What is the v 07 Mar 2019, 07:02
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There's a 5-sided polygon...
90+90+5k+6k+180-2k = 540 ( 180(n-2))
360+9k = 540
9k = 180
K= 20

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GMATinsight
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Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
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In the figure shown, all angles are measured in degrees. What is the v 07 Mar 2019, 07:13
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fskilnik
GMATH practice exercise (Quant Class 1)



In the figure shown, all angles are measured in degrees. What is the value of k?

(A) 18
(B) 20
(C) 22
(D) 25
(E) 27
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The answer os explained in attached file

Answer: Option E
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File comment: www.GMATinsight.com
Screenshot 2019-03-07 at 7.42.25 PM.png
Screenshot 2019-03-07 at 7.42.25 PM.png [ 525.95 KiB | Viewed 1868 times ]

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fskilnik
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In the figure shown, all angles are measured in degrees. What is the v 07 Mar 2019, 08:30
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Thank you both for your contributions!

I guess this (good!) solution was motivated by the two given right angles...

Could someone provide an alternate solution, without taking these right angles into account?

I mean: if m and n are parallel and all angles are measured in degrees, what is the value of k?



(Please do not create the "distance between the parallels" line used before... I want ANOTHER solution, based on triangles and parallelism, only...)

I will give a kudos for the first correct one provided!

Regards,
Fabio.
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In the figure shown, all angles are measured in degrees. What is the v 07 Mar 2019, 10:22
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The original problem was successfully solved in previous posts.

We will present below the "alternate version" with one possible solution!

fskilnik
GMATH practice exercise (Quant Class 1)



In the figure shown, if lines m and n are parallel and all angles are measured in degrees, what is the value of k?

(A) 18
(B) 20
(C) 22
(D) 25
(E) 27
Show more




\(? = k\,\,\,\left[ {{\rm{degrees}}} \right]\)

\(\left( {5k\,\,{\rm{is}}\,\,{\rm{exterior}}\,\,{\rm{angle}}\,{\rm{for}}\,\,\Delta } \right)\,\,\,:\,\,\,\,5k = \left( {180 - 6k} \right) + \left( {k + k} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,9k = 180\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {\rm{B}} \right)\)


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio
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