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

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Director
Joined: 07 Jan 2018
Posts: 555
Followers: 4

Kudos [?]: 482 [2] , given: 84

The logo of a certain corporations is in the shape of a poly [#permalink]  17 Feb 2018, 08:13
2
KUDOS
00:00

Question Stats:

60% (01:25) correct 40% (02:49) wrong based on 5 sessions
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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polygon.png [ 6.08 KiB | Viewed 292 times ]

Director
Joined: 07 Jan 2018
Posts: 555
Followers: 4

Kudos [?]: 482 [2] , given: 84

Re: The logo of a certain corporations is in the shape of a poly [#permalink]  20 Feb 2018, 01:53
2
KUDOS
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
_________________

This is my response to the question and may be incorrect. Feel free to rectify any mistakes

Manager
Joined: 15 Feb 2018
Posts: 53
Followers: 1

Kudos [?]: 17 [0], given: 33

Re: The logo of a certain corporations is in the shape of a poly [#permalink]  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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