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The logo of a certain corporations is in the shape of a poly

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Director
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The logo of a certain corporations is in the shape of a poly [#permalink] New post 17 Feb 2018, 08:13
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The logo of a certain corporation is in the shape of a polygon, where all angles of the polygon have equal measures. In the figure, V is one vertex of the polygon. If Y, in degrees is the measure of an angle of the polygon and y = 5x, how many sides does the polygon have?

A)5
B)6
C)10
D)12
E)30
[Reveal] Spoiler: OA

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2 KUDOS received
Director
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Re: The logo of a certain corporations is in the shape of a poly [#permalink] New post 20 Feb 2018, 01:53
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an angle of a regular polygon is given by a formula \(\frac{(n-2)*180}{n}\)
Hence we have y = \(\frac{(n-2)*180}{n}\)
here, \(n\) = no of sides of the polygon
\(X\) here is an external angle of the polygon

external angles of a regular polygon add up to 360 degrees
therefore \(x = 360/n\)
Given that,
\(y = 5X\)

\(5X =\) \(\frac{(n-2)*180}{n}\)

\(5X*n = (n-2)*180\)

\(5* 360 = (n-2)*180\)

solve for n; \(n = 12\)
option D
_________________

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Manager
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Re: The logo of a certain corporations is in the shape of a poly [#permalink] New post 22 Feb 2018, 13:13
Nice solution!

amorphous wrote:
an angle of a regular polygon is given by a formula \(\frac{(n-2)*180}{n}\)
Hence we have y = \(\frac{(n-2)*180}{n}\)
here, \(n\) = no of sides of the polygon
\(X\) here is an external angle of the polygon

external angles of a regular polygon add up to 360 degrees
therefore \(x = 360/n\)
Given that,
\(y = 5X\)

\(5X =\) \(\frac{(n-2)*180}{n}\)

\(5X*n = (n-2)*180\)

\(5* 360 = (n-2)*180\)

solve for n; \(n = 12\)
option D
Re: The logo of a certain corporations is in the shape of a poly   [#permalink] 22 Feb 2018, 13:13
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