How to find the number of sides of a polygon when given the interior angle sum?
Polygons are closed curves made of line segments. The polygons with equal sides and angles are called regular polygons. Each polygon has a fixed sum of interior angles depending on its number of sides.
Answer: To find the number of sides of a polygon when given the sum of interior angles, we use the formula: Sum of interior angles = (n - 2) × 180, where n is the number of sides.
Let's understand this, with the help of an example.
We use the formula: Sum of interior angles = (n - 2) × 180, where n is the number of sides of the polygon, to solve the problem.
Now, let's assume we have an interior angle sum of 1620. We have to find the number of sides the polygon has.
Hence, using the above equation, (n - 2) × 180 = 1620.
Now, n - 2 = 1620 / 180.
Therefore, n - 2 = 9.
Finally, n = 11.
Hence, it is an 11-sided polygon.