How To Find Interior Angles Of A Polygon Formula

Hence we can say if a polygon is convex then the sum of the degree measures of the exterior angles one at each vertex is 360.

How to find interior angles of a polygon formula. You also are able to recall a method for finding an unknown interior angle of a polygon by subtracting the known interior angles from the calculated sum. The interior angles of a polygon always lie inside the polygon. Interior angles of a polygon formula.

Interior angles of a regular polygon 180 n. You can only use the formula to find a single interior angle if the polygon is regular. An interior angle is an angle inside a shape.

The measure of each interior angle of an equiangular n gon is. Make sure each triangle here adds up to 180 and check that the pentagon s interior angles add up. The sum of the measures of the interior angles of a polygon with n sides is n 2 180.

The formula can be obtained in three ways. Consider for instance the ir regular pentagon below. If you count one exterior angle at each vertex the sum of the measures of the exterior angles of a polygon is always 360.

If n is the number of sides of a polygon then the formula is given below. The following diagram shows the formula for the sum of interior angles of an n sided polygon and the size of an interior angle of a n sided regular polygon. The formula for finding the sum of the interior angles of a polygon is devised by the basic ideology that the sum of the interior angles of a triangle is 180 0 the sum of the interior angles of a polygon is given by the product of two less than the number of sides of the polygon and the sum of the interior angles of a triangle.

Sum of interior angles of a polygon formula. Scroll down the page for more examples and solutions on the interior angles of a polygon. You can tell just by looking at the picture that angle a and angle b are not congruent.