Question

the exterior angle of a regular polygon is one third of its interior angle how many sides has his polygon​

Answer 1

Answer:

8 sides

Step-by-step explanation:

Sum of interior angles of a polygon with n sides is 180° × ( n - 2 ), so the interior angle of our regular polygon with n sides is

180 (n-2) / n

Exterior angle and interior angle make a straight line together, so they are supplementary.  That is, they add up to 180°.  So exterior angle is

180 - 180 (n-2) / n

We're told this is one third the interior angle so

180 - 180 (n-2) / n = (1/3) 180 (n-2) / n

=> 1 - (n-2) / n = (1/3) (n-2) / n    [ divided by 180 ]

=> 3n - 3(n-2) = n - 2       [ multiplied by 3n ]

=> 6 = n - 2

=> n = 8

[ Check: Internal angle = 180 (8-2)/8 = 135, external angle = 180-135 = 45, one third of 135 is 135/3 = 45 ]