Interior Angles Of A Convex Polygon

A polygon has the same number of interior angles as it does sides.

Interior angles of a convex polygon. 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. The sum of the interior angles of a polygon is given by the formula. 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.

Interior angles of a regular polygon 180 n 360 n. Let us discuss the three different formulas in detail. A polygon will have the number of interior angles equal to the number of sides it has.

If n is the number of sides of a polygon then the formula is given below. The interior angles of any polygon always add up to a constant value which depends only on the number of sides. The formula can be obtained in three ways.

If a polygon has 5 sides it will have 5 interior angles. Remember a convex polygon has no angles that point inward whereas a concave polygon makes something that looks like a cave where angles point toward the interior of the polygon. Note that a triangle 3 gon is always convex.

A convex polygon is defined as a polygon with all its interior angles less than 180. Think of it as a bulging polygon. This video provides the student with a walkthrough on interior angles in convex polygons.

The interior angles of a polygon always lie inside the 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. This means that all the vertices of the polygon will point outwards away from the interior of the shape.