How do you find the sum of interior angles of a multi-sided polygon?

To find the sum of the interior angles of a multi-sided polygon, the formula used is based on the number of sides, denoted as ( n ). The correct formulation is:

Sum of interior angles = ( (n - 2) \times 180 )

This formula originates from the basic principle in geometry that a polygon can be divided into triangles. For any polygon with ( n ) sides, you can create ( (n - 2) ) triangles. Each triangle has interior angles that sum up to 180 degrees. Therefore, by multiplying the number of triangles ( (n - 2) ) by the 180 degrees per triangle, you derive the total sum of the interior angles of the polygon.

Using this understanding, let's clarify why the other options do not provide the correct sum of interior angles.

The choice that suggests ( n \times 180 ) incorrectly implies that the sum of the angles is directly proportional to the number of sides without accounting for the partitioning into triangles.

The formulation ( (n + 2) \times 180 ) is also erroneous because adding 2 to the number of sides does not reflect the actual relationship to the angles; rather, it detracts from the