If the interior angle of a regular polygon is double the exterior angle then the polygon is
It is given that the polygon is regular. So all the sides and angles of the polygon are equal.
Let exterior angle = e° ⇒ Interior angle = 2e°
In a polygon, the sum of an interior angle and its respective exterior angle is 180°
⇒ interior angle + exterior angle = 180°
⇒ 2e + e = 180°
⇒ 3e = 180°
⇒ e = 60°
∴ exterior angle = 60°
∵ Sum of exterior angles of any polygon = 360∘
⇒ n × exterior angle = 360∘ (where, n= Number of sides)
⇒ n =360°exterior angle
∵ Number of sides of polygon is 6, so the given polygon is hexagon.