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# The logo of a certain corporation is in the shape of a polyg

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The logo of a certain corporation is in the shape of a polyg [#permalink]

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08 Jan 2013, 21:30
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The logo of a certain corporation is in the shape of a polygon, where all angles of a the polygon have equal measures. In the above 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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Last edited by fozzzy on 09 Jan 2013, 07:13, edited 3 times in total.
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Re: The logo of a corporation [#permalink]

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08 Jan 2013, 22:41
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From figure.,

x + y = 180
6*x = 180
x = 30, y = 150

Let number of sides be "n", hence number of interior angles is also "n"
Sum of all interior angles = 150*n
Formula for sum of interior angles = 180*(n-2)

180*(n-2) = 150*n
30*n = 360

n = 360/30 = 12

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Re: The logo of a certain corporation is in the shape of a polyg [#permalink]

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06 Jan 2014, 01:47
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Hi thegame001.,

The question states that all the angles of the polygon are equal.

Since there are n sides and hence 'n' angles, the sum of all the angles is 150 added 'n' times and that is 150n.

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Re: The logo of a corporation [#permalink]

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09 Jan 2013, 02:29
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fozzzy wrote:
MacFauz wrote:
From figure.,

x + y = 180
6*x = 180
x = 30, y = 150

Let number of sides be "n", hence number of interior angles is also "n"
Sum of all interior angles = 150*n
Formula for sum of interior angles = 180*(n-2)

180*(n-2) = 150*n
30*n = 360

n = 360/30 = 12

How did you get that step, I'm really bad at geometry...

We are given y = 5x in the question statement. The two angles are supplementary (the two different angles made by the same line with another line) and hence add up to 180.
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Re: The logo of a corporation [#permalink]

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09 Jan 2013, 21:29
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shanmugamgsn wrote:
MacFauz wrote:
From figure.,

x + y = 180
6*x = 180
x = 30, y = 150

Let number of sides be "n", hence number of interior angles is also "n"
Sum of all interior angles = 150*n
Formula for sum of interior angles = 180*(n-2)

180*(n-2) = 150*n
30*n = 360

n = 360/30 = 12

hi MacFauz,

x + y = 180
6*x = 180
x = 30, y = 150

i did this way 360/30 = 12 (since all angels are equal)
I guess this will not work out in all cases !

Also how u figured out this ?
Sum of all interior angles = 150*n

There are "n" sides and since the figure is a polygon, there are "n" angles. Each interior angle is 150. So sum of all interior angles is 150 added "n" times or 150*n
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Re: The logo of a corporation [#permalink]

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21 Feb 2013, 07:59
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Hi vinaymimani.,

That was actually shanmugamgsn's solution.. Great if it is correct.. But I would have needed to used the (n-2)*180 formula since I did not know that sum of all exterior angles of a polygon is 360.. I have not heard of that before... Can you please illustrate the same in cases of a rectangle and triangle?

Incase of a rectangle, the external angle for each side is (180-90)degrees = 90 degrees. And there are 4 such angles. Thus the total sum of the external angles is 90*4 = 360 degrees.

Incase of a triangle, let the 3 angles be a,b,c. a+b+c = 180 degrees.Now, the respective exterior angles are : 180-a, 180-b,180-c. Thus, their sum is 180*3-(a+b+c) = 180*2 = 360 degrees.

I hope it's clear now. Once again, we can only divide 360 degrees by 30 degrees in this problem only because it is a regular polygon.
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Re: The logo of a certain corporation is in the shape of a polyg [#permalink]

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15 Dec 2013, 17:36
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For a polygon with 'n' sides, the sum of the interior angles is 180*(n-2)

For example, a triangle has 3 sides. So the sum of the interior angles is 180*(3-2) = 180

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The logo of a certain corporation is in the shape of a polyg [#permalink]

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23 Aug 2015, 01:51
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Here's a quicker way.

y + x = 180
y = 5x
Hence, x = 30

Exterior angle, x = 360/n (since all angles are equal)
n= 360/30
n = 12

Hope this helps.
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Re: The logo of a corporation [#permalink]

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08 Jan 2013, 22:56
Ans D

Explaination same as Macfauz...
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Re: The logo of a corporation [#permalink]

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09 Jan 2013, 02:24
MacFauz wrote:
From figure.,

x + y = 180
6*x = 180
x = 30, y = 150

Let number of sides be "n", hence number of interior angles is also "n"
Sum of all interior angles = 150*n
Formula for sum of interior angles = 180*(n-2)

180*(n-2) = 150*n
30*n = 360

n = 360/30 = 12

How did you get that step, I'm really bad at geometry...
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Re: The logo of a corporation [#permalink]

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09 Jan 2013, 20:33
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MacFauz wrote:
From figure.,

x + y = 180
6*x = 180
x = 30, y = 150

Let number of sides be "n", hence number of interior angles is also "n"
Sum of all interior angles = 150*n
Formula for sum of interior angles = 180*(n-2)

180*(n-2) = 150*n
30*n = 360

n = 360/30 = 12

hi MacFauz,

x + y = 180
6*x = 180
x = 30, y = 150

i did this way 360/30 = 12 (since all angels are equal)
I guess this will not work out in all cases !

Also how u figured out this ?
Sum of all interior angles = 150*n
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Re: The logo of a certain corporation is in the shape of a polyg [#permalink]

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18 Feb 2013, 05:22
fozzzy wrote:
The logo of a certain corporation is in the shape of a polygon, where all angles of a the polygon have equal measures. In the above 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

x+y = 180 (straight line)
x+5x= 180. x=30.

Interior angle of polygon = 30 x 5 = 150.

Interior Angle of regular polygon with side n no. of sides = (2n -4) * 90 / n
150 = (2n -4) * 90 / n. Solve it. n = 12.
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Re: The logo of a corporation [#permalink]

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21 Feb 2013, 06:55
shanmugamgsn wrote:
MacFauz wrote:
From figure.,

x + y = 180
6*x = 180
x = 30, y = 150

Let number of sides be "n", hence number of interior angles is also "n"
Sum of all interior angles = 150*n
Formula for sum of interior angles = 180*(n-2)

180*(n-2) = 150*n
30*n = 360

n = 360/30 = 12

hi MacFauz,

x + y = 180
6*x = 180
x = 30, y = 150

i did this way 360/30 = 12 (since all angels are equal)
I guess this will not work out in all cases !

Basically what you have done(in red) is actually true for all regular polygons. We have the exterior angle as 30 degrees from the problem.Also, the sum of all the exterior angles in case of any polygon(regular/not regular) is always 360 degrees. As it is mentioned that this is a regualr polygon, only because of that, you can divide and get the answer as 12. Thus using the formula (n-2)*180 is not necessary, atleast in this problem.
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Re: The logo of a corporation [#permalink]

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21 Feb 2013, 07:50
vinaymimani wrote:
shanmugamgsn wrote:
MacFauz wrote:
From figure.,

x + y = 180
6*x = 180
x = 30, y = 150

Let number of sides be "n", hence number of interior angles is also "n"
Sum of all interior angles = 150*n
Formula for sum of interior angles = 180*(n-2)

180*(n-2) = 150*n
30*n = 360

n = 360/30 = 12

hi MacFauz,

x + y = 180
6*x = 180
x = 30, y = 150

i did this way 360/30 = 12 (since all angels are equal)
I guess this will not work out in all cases !

Basically what you have done(in red) is actually true for all regular polygons. We have the exterior angle as 30 degrees from the problem.Also, the sum of all the exterior angles in case of any polygon(regular/not regular) is always 360 degrees. As it is mentioned that this is a regualr polygon, only because of that, you can divide and get the answer as 12. Thus using the formula (n-2)*180 is not necessary, atleast in this problem.

Hi vinaymimani.,

That was actually shanmugamgsn's solution.. Great if it is correct.. But I would have needed to used the (n-2)*180 formula since I did not know that sum of all exterior angles of a polygon is 360.. I have not heard of that before... Can you please illustrate the same in cases of a rectangle and triangle?
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Re: The logo of a certain corporation is in the shape of a polyg [#permalink]

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17 Nov 2013, 18:11
Very simple. $$y=(n-2)180/n$$. $$x=180-[(n-2)180/n]$$. Given y=5x. Substitute and solve for n.
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Re: The logo of a certain corporation is in the shape of a polyg [#permalink]

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17 Nov 2013, 18:14
Hint: After equating 180 is cancelled throughout the equation. This makes calculations very easy.
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Re: The logo of a corporation [#permalink]

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15 Dec 2013, 06:41
MacFauz wrote:
Formula for sum of interior angles = 180*(n-2)

Why does this apply? Why n-2? I understand that the degrees of x + y = 180, but what relevance does that have in regards to the above 180*(n-2)?

I don't understand.
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Re: The logo of a corporation [#permalink]

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05 Jan 2014, 23:54
MacFauz wrote:
From figure.,

x + y = 180
6*x = 180
x = 30, y = 150

Let number of sides be "n", hence number of interior angles is also "n"
Sum of all interior angles = 150*n
Formula for sum of interior angles = 180*(n-2)

180*(n-2) = 150*n
30*n = 360

n = 360/30 = 12

Can you tell me why

Sum of all interior angles = 150*n?

Are all the angles equal?
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