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

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

• A. Sum = (n + 2) x 180
• B. Sum = (n - 2) x 180
• C. Sum = n x 180
• D. Sum = 360 degrees

Answer: (D)

The sum of the exterior angles of any polygon, regardless of the number of sides, is always 360 degrees. This holds true for polygons with three sides (triangles) to those with hundreds of sides. When considering exterior angles, the definition is that these are the angles formed between one side of the polygon and the extension of its adjacent side. As you traverse the perimeter of the polygon, the exterior angles formed will always sum up to a complete turn, which equals 360 degrees. Understanding that this property is universal applies across all types of polygons reinforces the concept. While the other formulas relate to the calculation of interior angles or characteristics of specific types of polygons, they do not pertain to the total of exterior angles. Hence, the correct approach for determining the overall sum of exterior angles remains consistently grounded at 360 degrees.

The sum of the exterior angles of any polygon, regardless of the number of sides, is always 360 degrees. This holds true for polygons with three sides (triangles) to those with hundreds of sides.

When considering exterior angles, the definition is that these are the angles formed between one side of the polygon and the extension of its adjacent side. As you traverse the perimeter of the polygon, the exterior angles formed will always sum up to a complete turn, which equals 360 degrees.

Understanding that this property is universal applies across all types of polygons reinforces the concept. While the other formulas relate to the calculation of interior angles or characteristics of specific types of polygons, they do not pertain to the total of exterior angles. Hence, the correct approach for determining the overall sum of exterior angles remains consistently grounded at 360 degrees.