Question

the ratio between an exterior angle and interior angle of a regular polygon 2:3. Find the number of sides in the polygon.

Answer 1

A regular polygon implies all the angles of polygon are equal
the sum of exterior and interior angles of a polygon must be equal to 180 degrees
we have seen that interior and exterior angles are 2:3
so lets say 2x+3x = 180
5x = 180 
x = 36
so the interior angle = 3x = 108
the number of sides of polygon can be obtained by dividing 360 with exterior angle
360/72 = 5
hence it is a pentagon