What Is The Sum Of A Polygon’S Internal Angles?

The general rule for calculating the sum of interior angles in a polygon is to add another 180° to the total when adding a side. In a regular polygon, each angle equals to the other, and all interior angles are equal to each other. There are two types of interior angles formed when two straight lines are cut by a transversal: alternate interior angles and co-interior angles.

The sum of interior angles of a polygon can be calculated using the formula S= (n-2) times 180^(circ) where n is the number of sides. For example, a pentagon has 5 sides, so its interior angle sum is (5 – 2) x 180° = 3 x 180° = 540°. To find the sum of interior angles, multiply the number of triangles formed inside the polygon to 180 degrees.

In quadrilaterals, the interior angles in a triangle add up to 180°, while for a square they add up to 360°. The sum of all interior angles of a regular polygon is calculated by the formula S=(n-2) × 180°, where n is the number of sides. To determine the sum of internal angles of a polygon, take the number of sides on the polygon, subtract 2 and multiply by 180 degrees.

At each vertex of the polygon, the interior and exterior angles form a linear pair. Since there are n vertices, there will be n linear pairs in total. The formula for calculating the sum of interior angles is (n – 2) × 180 ∘, where n is the number of sides. All the interior angles in a regular polygon are equal.