Interior Angles Of A Convex Polygon

This video provides the student with a walkthrough on interior angles in convex polygons.

Interior angles of a convex polygon. Interior angle of a polygon is that angle formed at the point of contact of any two adjacent sides of a polygon. In order to find the measure of a single interior angle of a regular polygon a polygon with sides of equal length and angles of equal measure with n sides we calculate the sum interior angles or n 2 180 and then divide that sum by the number of sides or n. A convex polygon is defined as a polygon with all its interior angles less than 180.

The interior angles of a polygon always lie inside the polygon. The sum of the interior angles of a polygon is given by the formula. In a convex polygon all interior angles are less thaedmjg n or equal to 180 degrees while in a strictly convex polygon all interior angles are strictly less than 180 degrees.

Note that a triangle 3 gon is always convex. This is part of ck 12 s basic geometry. The formula can be obtained in three ways.

Let us discuss the three different formulas in detail. And a regular polygon is one that is both equilateral all sides are congruent and equiangular all angles are congruent. If n is the number of sides of a polygon then the formula is given below.

This means that all the vertices of the polygon will point outwards away from the interior of the shape. The interior angles of any polygon always add up to a constant value which depends only on the number of sides. For example the interior angles of a pentagon always add up to 540 no matter if it regular or irregular convex or concave or what size and shape it is.

The sum of the interior angles in a polygon depends on the number of sides it has. Interior angles in convex polygons the interior angle of a polygon is one of the angles on the inside as shown in the picture below. Interior angles of a regular polygon 180 n 360 n.