Question 464025
Let be x degree the measure of an exterior angle, then the measure of an interior 

angle is 2x degree. Assume that the regular polygon has n sides (or angles).

We know that the sum of the interior angles is :{{{n*2x=(n-2)*180}}} and the sum

of exterior angles is:{{{n*x=360}}} <=> {{{x=360/n}}}, substituting this value 

for x in the first equation we get:{{{n*2*360/n=(n-2)*180}}} <=>

{{{4*180=(n-2)*180}}}<=>{{{4=n-2}}} <=>{{{n=6}}}. Since the number of angles is 

six, our regular polygon is a hexagon, and the number of diagonals drawn from one 

vertex is three less then the number of sides, 6-3=3 diagonals.