The Formula for Calculating the Sum of Interior Angles in Regular Polygons

Interior Angles

Interior angles are angles formed inside a polygon, between two adjacent sides

Interior angles are angles formed inside a polygon, between two adjacent sides. In other words, when you have a polygon with n sides, the interior angles are the angles formed between each pair of adjacent sides.

The sum of the interior angles of a polygon depends on the number of sides it has. Let’s consider a regular polygon, which is a polygon with all sides and angles equal.

To find the sum of the interior angles of a regular polygon, you can use the formula:

Sum of interior angles = (n-2) * 180 degrees

In this formula, n represents the number of sides of the polygon.

For example, let’s consider a triangle. A triangle has 3 sides (n = 3). Plugging this into the formula, we get:

Sum of interior angles = (3-2) * 180 degrees = 1 * 180 degrees = 180 degrees

So, the sum of the interior angles of a triangle is 180 degrees. Each interior angle of a triangle is 60 degrees.

Similarly, let’s consider a square. A square has 4 sides (n = 4). Using the formula, we get:

Sum of interior angles = (4-2) * 180 degrees = 2 * 180 degrees = 360 degrees

So, the sum of the interior angles of a square is 360 degrees. Each interior angle of a square is 90 degrees.

This formula can be used to find the sum of the interior angles of any regular polygon, regardless of the number of sides.

Remember, this formula only applies to regular polygons, where all the sides are equal. If you have an irregular polygon, where the sides and angles are not equal, it becomes more complicated to find the sum of the interior angles. Each interior angle will vary depending on the shape of the polygon. In that case, you may need to break the irregular polygon into smaller triangles or other regular polygons to find the sum of the interior angles.

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