Interior Angles of Different Shapes

An interior angle is the angle formed when the endpoints of a polygon’s two sides are shared. In simple terms, when a new line intersects two straight lines that are parallel, then four angles will be formed inside them. These angles are known as Interior Angles. This angle will be inside a shape always. Also the angles formed outside the shape are known as exterior angles. Interior angles are sometimes referred as “Internal Angles”.

Interior Angles of a Triangle
The interior angles of a triangle will always be 180 degrees. For example if A, B and C are three sides of a triangle, then A+B+C = 180 degrees. Due to this reason, only one of the angles formed inside a triangle can be obtuse (i.e. greater than 90 degree). Eventually in a right angle triangle, since one angle is 90 degree, the other two angles will always add up to 90 degree.

Interior Angles of Square and Quadrilaterals
A square can be made up of two triangles. Hence, the sum of interior angles of square will add up to 360 degrees.  Quadrilateral also lies in the same case in which the sum of interior angles gives 360 degrees. Meanwhile, in this case maximum of two angles can be greater than 90 degrees.
Interior Angles of Polygons

The interior angle of polygon is nothing but the angle formed at every vertex inside it. Hence for a polygon of N vertices and N sides, there will be N interior angles. The sum of these interior angles will sum up to a constant value always. The formula that relates the sum of interior angles and number of sides of polygon is as follows:
Sum of Interior Angles = 180(n-2) degrees, where n is the number of sides. For example, sum of square that has four sides will be 180*2= 360 degrees, sum of pentagon which has five sides will be 540 degrees. Similarly Interior Angles of a hexagon, which has six sides, will be 720 degrees.
Also, the above said formula will not be applied to regular polygons, whose all sides and interior angles are always equal. Therefore, Interior Angles formula for a regular polygon will be 180(n-2) divided by n, where ‘n’ is the number of sides. This formula applies to its children such as regular pentagon whose angle is 108 degree, regular hexagon whose interior angle is 120 degree etc.
Also, two interior Angles at the same side of a polygon located at both sides are referred as “Adjacent Interior Angles”.