Question

the exterior angle of a regular polygon is 1/3 of its interior anglehow many sides does the polygon has

Answer 1

3x+x =4x

so 4x=180

so x=45

no of sides are=360/45

=8 sides

hence it is octagon

Answer 2

Let the measure of interior angle of the polygon be x then its exterior will be x/3

But since they form a linear pair
x +x/3 = 180
4x/3=180
x=135°

Now let the no. of sides of polygon be n

So, 180(n-2) = 135n
180n -360= 135n
45n=360
n= 8

So no. of sides of polygon are 8 i.e. polygon is an octagon.

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