Answer :
To find the sum of all the angles of an n-sided polygon (where n is a natural number), there's a straightforward formula that can be used. The formula is:
Sum of all interior angles of an n-sided polygon = (n - 2) × 180°
This formula comes from the fact that any polygon can be split into triangles (which each sum up to 180°) by drawing diagonals from one vertex to all other vertices not directly adjacent to it. The number of triangles that can be created this way is always two less than the number of sides of the polygon.
Let's apply this formula to find the sum of all the angles of an 11-sided polygon:
Given n = 11 (since it's an 11-sided polygon),
Sum of angles = (11 - 2) × 180°
= 9 × 180°
= 1620°
Therefore, the sum of all the angles of an 11-sided polygon is 1620 degrees.
