Question

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.

a) the sum of the angles of a square is 360°.
b) the sum of the angles of a square is 1,440°.
c) the sum of the angles of a square is 1,080°.
d) the sum of the angles of a square is 182°.

Answer 1

The interior angle sum of a regular polygon with n sides can be found using the formula (n-2) * 180 degrees. Applying this formula to a square, we find that the sum of the angles is indeed 360 degrees. Therefore, the correct option is a) the sum of the angles of a square is 360°.

Step-by-step explanation:

To develop the interior angle sums of regular polygons formula, we can start with a triangle. We know that a triangle has three angles that add up to 180 degrees. Now, if we take a regular polygon with n sides, we can divide it into n-2 triangles by drawing diagonals from one vertex to all other vertices except the adjacent ones. Each of these triangles has interior angles summing up to 180 degrees. Therefore, the interior angle sum of a regular polygon with n sides is (n-2) * 180 degrees.

To test this formula, let's consider a square. A square has four sides, so n = 4. Substituting this value into the formula, we get (4-2) * 180 = 2 * 180 = 360 degrees. Therefore, the correct option is a) the sum of the angles of a square is 360°.