What is the internal angle sum of a polygon with eight sides?

What is the internal angle sum of a polygon with eight sides?

• A. 360 degrees
• B. 540 degrees
• C. 720 degrees
• D. 1080 degrees

Answer: (C)

To determine the internal angle sum of a polygon, you can use the formula: \[ \text{Sum of interior angles} = (n - 2) \times 180 \] where \( n \) is the number of sides in the polygon. In this case, the polygon has eight sides, so you substitute \( n \) with 8: \[ \text{Sum of interior angles} = (8 - 2) \times 180 = 6 \times 180 = 1080 \text{ degrees} \] This calculation shows that the internal angle sum of an eight-sided polygon (octagon) is indeed 1080 degrees. Each angle within the polygon contributes to this total, ensuring that the angles fit together properly to form the shape. Understanding this formula is essential in geometry, especially when analyzing the properties of different polygons.

To determine the internal angle sum of a polygon, you can use the formula:

[

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

]

where ( n ) is the number of sides in the polygon. In this case, the polygon has eight sides, so you substitute ( n ) with 8:

[

\text{Sum of interior angles} = (8 - 2) \times 180 = 6 \times 180 = 1080 \text{ degrees}

]

This calculation shows that the internal angle sum of an eight-sided polygon (octagon) is indeed 1080 degrees. Each angle within the polygon contributes to this total, ensuring that the angles fit together properly to form the shape. Understanding this formula is essential in geometry, especially when analyzing the properties of different polygons.