Question

The interior angle of a regular polygon is twice the exterior angle how many sides has the polygon

Answer 1

To find the number of sides in a regular polygon where the interior angle is twice the size of the exterior angle, we solve the equation 3x = 180 degrees to find the exterior angle size, which is 60 degrees. Then, we divide 360 degrees by 60 degrees to conclude that the polygon has 6 sides, meaning it is a hexagon.

Step-by-step explanation:

The question asks us about the properties of a regular polygon where the interior angle is twice the size of the exterior angle. To find the number of sides of such a polygon, we can use the relationship that the sum of the interior and exterior angles at any vertex of a polygon is always 180 degrees. Since we know that the interior angle is twice the exterior angle (let's denote the exterior angle as x), we have the equation:

Interior Angle + Exterior Angle = 180 degrees

2x + x = 180 degrees

3x = 180 degrees

x = 60 degrees

Now, since exterior angles of a regular polygon sum up to 360 degrees, we can find the number of sides by dividing 360 degrees by the measure of one exterior angle:

360 degrees / 60 degrees per angle = 6 sides

Therefore, a regular polygon where the interior angle is twice the exterior angle must have 6 sides, and thus, it is a hexagon.

Answer 2

6 sides

Step-by-step explanation:

the interior angle + the exterior angle = 180°

let x be the exterior angle then 2x is the interior angle and

x + 2x = 180

3x = 180 ( divide both sides by 3 )

x = 60

the exterior angle = 60°

the sum of the exterior angles of a polygon = 360°

since the polygon is regular the the exterior angles are congruent, then

number of sides = 360° ÷ 60° = 6