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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, 20:30

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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?

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

Answer is D
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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

Answer is D

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

Answer is D

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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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

Answer is D

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 _________________

GMAT - Practice, Patience, Persistence Kudos if u like

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

Answer is D

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

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18 Feb 2013, 04:22

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.
_________________

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

Answer is D

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.
_________________

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

Answer is D

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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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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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)

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

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18 Nov 2017, 06:49

While I would like to stay away from high level math and formulas, it helps to remember few formulas in case of Geometry questions. There are two pertinent flavors of the same formula that one should remember:

1 - sum of interior angles of a polygon with n sides = 180 * (n - 2) 2 - Measure of each angle of a regular polygon* = \(\frac{[180 * (n - 2) ]}{n}\)

A regular polygon* is a polygon that is equiangular* (all angles are equal in measure) and equilateral* (all sides have the same length) * https://en.wikipedia.org/wiki/Regular_polygon

So in this question, we have 2 simultaneous equations: