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The logo of a certain corporations is in the shape of a poly
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17 Feb 2018, 08:13
17 Feb 2018, 08:13
2
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Question Stats:
61% (01:45) correct
38% (03:14) wrong based on 13 sessions
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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
A)5
B)6
C)10
D)12
E)30
Attachments
polygon.png [ 6.08 KiB | Viewed 2164 times ]
Re: The logo of a certain corporations is in the shape of a poly
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20 Feb 2018, 01:53
20 Feb 2018, 01:53
2
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
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
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
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
