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# A regular convex polygon has 'n' sides. What is the value of n?

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DS Forum Moderator
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A regular convex polygon has 'n' sides. What is the value of n?  [#permalink]

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25 Jun 2018, 10:02
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A regular convex polygon has 'n' sides. What is the value of n?

(1) Difference between interior and exterior angle of this polygon is 60 degrees.

(2) Sum of interior and exterior angle of this polygon is 180 degrees.
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Joined: 24 Jun 2018
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Re: A regular convex polygon has 'n' sides. What is the value of n?  [#permalink]

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25 Jun 2018, 11:17
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amanvermagmat wrote:
A regular convex polygon has 'n' sides. What is the value of n?

(1) Difference between interior and exterior angle of this polygon is 60 degrees.

(2) Sum of interior and exterior angle of this polygon is 180 degrees.

statement 1- Difference between interior and exterior angle of this polygon is 60 degrees. insufficient
statement 2- Sum of interior and exterior angle of this polygon is 180 degrees. insufficient.

However taking the interior angle as x and exterior as y we can make 2 equation
x-y= 60
x+y= 180

solving these two statements will give x as 120, from this we can deduce that the polygon has 6 sides

Hence choice C

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Re: A regular convex polygon has 'n' sides. What is the value of n?  [#permalink]

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26 Jun 2018, 02:04
Interior angle of a regular polygon = (n-2)180/n = 180 - 360/n
Exterior angle of a regular polygon = 360/n

Option 1:

difference between Interior and Exterior angle = 60;

180-360/n-360/n = 60
: 120 = 720/n
: n =6;

Hence Option is SUFFICIENT.

Option 2 :

sum of interior and exterior angle = 180.
This is a fundamental property and hence cannot be used to determine number of sides of a polygon.

This Option is INSUFFICIENT.

Thus the answer will be : A.
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Re: A regular convex polygon has 'n' sides. What is the value of n?  [#permalink]

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27 Jun 2018, 10:14
amanvermagmat wrote:
A regular convex polygon has 'n' sides. What is the value of n?

(1) Difference between interior and exterior angle of this polygon is 60 degrees.

(2) Sum of interior and exterior angle of this polygon is 180 degrees.

Lets say each interior angle of this regular polygon is I and each exterior angle is E. Its obvious that I + E = 180
So second statement doesnt tell us anything new, and is thus insufficient.

First statement uses the phrase 'difference between'. 'Difference between' I and E could mean either I-E or E-I

If we take the first case, I - E = 60 and use it with I + E = 180, we will get I = 120 and E = 60. Thus this is a regular hexagon
If we take the second case, E - I = 60 and use it with I + E = 180, we will get E = 120 and I = 60. Thus this becomes an equilateral triangle.

So n can be either 6 or 3. Not sufficient still. Hence E answer
Re: A regular convex polygon has 'n' sides. What is the value of n? &nbs [#permalink] 27 Jun 2018, 10:14
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