Use the angle sum of triangles to develop the interior angle sums of regular polygons formula using decomposition. Test the formula by finding the sum of the interior angles of a square.
The sum of the angles of a square is 1, 440)".
The sum of the angles of a square is 182"
The sum of the angles of a square is 1,080",
The sum of the angles of a square is 360°.
To develop the formula for the interior angle sum of regular polygons, we can start by using the angle sum of a triangle.
The angle sum of a triangle is always 180 degrees. A square can be divided into two congruent right triangles, so the sum of the interior angles of a square would be twice the angle sum of a triangle.
Angle sum of a square = 2 * Angle sum of a triangle
= 2 * 180°
= 360°
Therefore, the interior angle sum of a square is 360 degrees.
Now, let's test this formula by finding the sum of the interior angles of a square.
The formula states that the sum of the angles of a square is 360°.
So, the sum of the angles of a square is indeed 360°, which confirms the validity of the formula.