1. What is the sum of interior angles of any polygon?
2. What is the formula for the value of each interior angle of a regular polygon with n number of sides?
for a polygon with n sides, the sum is 180(n-2)
so, each angle is 180(n-2)/n
1. The sum of the interior angles of any polygon can be found using the formula: (n - 2) * 180 degrees, where n represents the number of sides of the polygon.
To understand how this formula is derived, let's start with the fact that the sum of the interior angles of a triangle is always 180 degrees. Now, let's consider a polygon with n sides. We can divide it into n-2 triangles by drawing n-2 non-intersecting diagonals from one vertex to the other vertices. Each triangle will have an interior angle sum of 180 degrees.
So, if we have n-2 triangles, the sum of their interior angles will be (n-2) * 180 degrees.
2. The formula for the value of each interior angle of a regular polygon with n sides is: (n-2) * 180 degrees / n.
To understand this formula, let's consider a regular polygon, which has equal side lengths and equal interior angles. Since all interior angles are equal, we can divide the sum of the interior angles by the number of sides to find the value of each interior angle.
Using the formula for the sum of interior angles of any polygon, which is (n - 2) * 180 degrees, we divide it by the number of sides, n, to get the value of each interior angle. So, the formula becomes: (n - 2) * 180 degrees / n.
For example, if we have a regular hexagon (a polygon with 6 sides), we can substitute n = 6 into the formula. Thus, each interior angle would be (6 - 2) * 180 degrees / 6 = 120 degrees.