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In the figure shown, all angles are measured in degrees. What is the v

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In the figure shown, all angles are measured in degrees. What is the v  [#permalink]

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New post 07 Mar 2019, 06:47
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GMATH practice exercise (Quant Class 1)

Image

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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In the figure shown, all angles are measured in degrees. What is the v  [#permalink]

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New post 07 Mar 2019, 07:02
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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Re: In the figure shown, all angles are measured in degrees. What is the v  [#permalink]

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New post 07 Mar 2019, 07:13
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fskilnik wrote:
GMATH practice exercise (Quant Class 1)

Image

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


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 382 times ]


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Re: In the figure shown, all angles are measured in degrees. What is the v  [#permalink]

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New post 07 Mar 2019, 08:30
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?

Image

(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  [#permalink]

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New post 07 Mar 2019, 10:22
The original problem was successfully solved in previous posts.

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

fskilnik wrote:
GMATH practice exercise (Quant Class 1)

Image

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


Image


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

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


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

Regards,
Fabio
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In the figure shown, all angles are measured in degrees. What is the v   [#permalink] 07 Mar 2019, 10:22
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