The sum of interior angles of a regular polygon is twice the sum of its exterior angles.
sum of all interior angles of a regular polygon= 180(n-2) where n is equal to the number of sides in the polygon.
sum of all exterior angles of a regular polygon = 360 degrees
according to question,


180(n-2) = 2×360
n-2= 2×360÷180
n-2 = 2×2
n-2=4
n=4+2
n=6

Number of sides =6

Problem: The sum of the interior angles of a regular polygon is twice the sum of the exterior angles. Find the number of sides of the polygon.

Solution:
To solve this problem, we need to use the formulas for the sum of the interior angles and the sum of the exterior angles of a polygon.

Sum of the Interior Angles:
The sum of the interior angles of a polygon can be found using the formula:
Sum of interior angles = (n - 2) * 180 degrees
where n is the number of sides of the polygon.

Sum of the Exterior Angles:
The sum of the exterior angles of any polygon is always 360 degrees. This can be proved by considering that the exterior angles of a polygon form a complete revolution around a point.

Now, let's use the given information that the sum of the interior angles is twice the sum of the exterior angles.

Step 1: Set up the equations
We have the following equations:
Sum of interior angles = (n - 2) * 180
Sum of exterior angles = 360

Step 2: Substitute the formulas into the equations
Substituting the formulas for the sum of the interior angles and the sum of the exterior angles into the equations, we have:
(n - 2) * 180 = 2 * 360

Step 3: Simplify and solve for n
Simplifying the equation, we get:
(n - 2) * 180 = 720
Divide both sides by 180 to isolate n:
n - 2 = 4
Add 2 to both sides:
n = 6

Step 4: Interpret the solution
The number of sides of the polygon is 6. Therefore, the polygon is a hexagon.

Summary:
The sum of the interior angles of a regular polygon is twice the sum of the exterior angles. By using the formulas for the sum of the interior angles and the sum of the exterior angles, we can set up an equation and solve for the number of sides of the polygon. In this case, the polygon has 6 sides, making it a hexagon.