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

Question

(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.

ReadyPlayerOne · Answer

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

KUDOS IF THIS WAS HELPFUL

sidsst · Answer

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.

amanvermagmat · Answer

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

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

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