How do you calculate the sum of the interior angles of a polygon with n sides?

How do you calculate the sum of the interior angles of a polygon with n sides?

• A. n * 180
• B. (n-2) * 180
• C. (n+2) * 180
• D. n * 90

Answer: (B)

The sum of the interior angles of a polygon can be calculated using the formula (n-2) * 180, where n represents the number of sides of the polygon. This formula derives from the fact that a polygon can be divided into triangles, and the sum of the interior angles of each triangle is always 180 degrees. To explain further, when you take a polygon with n sides and draw diagonals from one vertex to connect to the other non-adjacent vertices, you essentially create (n-2) triangles within the polygon. Each of these triangles contributes 180 degrees to the overall sum of the angles. Thus, by multiplying the number of triangles (which is n-2) by the 180 degrees from each triangle, you arrive at the total sum of the interior angles for that polygon. This understanding is crucial for various applications in geometry, including solving problems related to the properties of polygons and their angles, which are commonly encountered in grade-level mathematics.

The sum of the interior angles of a polygon can be calculated using the formula (n-2) * 180, where n represents the number of sides of the polygon. This formula derives from the fact that a polygon can be divided into triangles, and the sum of the interior angles of each triangle is always 180 degrees.

To explain further, when you take a polygon with n sides and draw diagonals from one vertex to connect to the other non-adjacent vertices, you essentially create (n-2) triangles within the polygon. Each of these triangles contributes 180 degrees to the overall sum of the angles. Thus, by multiplying the number of triangles (which is n-2) by the 180 degrees from each triangle, you arrive at the total sum of the interior angles for that polygon.

This understanding is crucial for various applications in geometry, including solving problems related to the properties of polygons and their angles, which are commonly encountered in grade-level mathematics.