Question 936025


The sum of {{{one}}} {{{exterior}}} angle and {{{one}}}{{{ interior}}} angle is {{{180}}} since they form a linear pair.

Let the {{{exterior}}} angle be {{{x}}}.

angles are in ratio {{{1:5}}}; so, the {{{interior}}} angle is {{{5x}}}.

Now
{{{x + 5x = 180}}}
{{{6x = 180}}}
{{{x=30}}}...the exterior angle is equal to {{{30}}}

The sum of the exterior angles of a regular polygon is {{{360}}}
So,we multiply the {{{exterior}}} angle by the number of the sides.

 {{{n * x = 360}}} where {{{n}}} is the no. of sides

{{{n * 30 = 360 }}}

{{{ n = 360/30}}}

{{{n=12}}}