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

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GMATH Teacher
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Joined: 12 Oct 2010
Posts: 935
In the figure shown, all angles are measured in degrees. What is the v  [#permalink]

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07 Mar 2019, 05:47
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60% (02:15) correct 40% (02:18) wrong based on 20 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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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
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In the figure shown, all angles are measured in degrees. What is the v  [#permalink]

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07 Mar 2019, 06:02
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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07 Mar 2019, 06:13
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fskilnik wrote:
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

The answer os explained in attached file

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

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07 Mar 2019, 07:30
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?

(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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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
In the figure shown, all angles are measured in degrees. What is the v  [#permalink]

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07 Mar 2019, 09:22
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)

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

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

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

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

Regards,
Fabio
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
In the figure shown, all angles are measured in degrees. What is the v   [#permalink] 07 Mar 2019, 09:22
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