What is the formula for a single interior angle of a regular polygon with n sides?

To find the formula for a single interior angle of a regular polygon with ( n ) sides, we first need to understand the relationship between the number of sides and the interior angles.

The sum of the interior angles of a polygon is given by the formula ( 180(n-2) ), where ( n ) is the number of sides. This formula arises because any polygon can be divided into ( n-2 ) triangles, and each triangle has a sum of interior angles equal to ( 180 ) degrees. Therefore, the total sum of the angles in the polygon is the number of triangles multiplied by ( 180 ).

To find the measure of a single interior angle in a regular polygon, which has all its angles equal, you divide the total sum of the interior angles by the number of sides ( n ):

[ \text{Interior angle} = \frac{180(n-2)}{n} ]

This is why the correct formula for a single interior angle of a regular polygon is given by ( (180(n-2))/n ).

This choice correctly represents the relationship between the number of sides in the polygon and the measures of its interior angles, leading to a clear understanding of how these