Angle measures in a polygon
The polygon is a closed plane figure which has straight sides. There is a method to measure sum of the interior angles which depends upon the number of sides (which is same as the number of angles).
The interior angles of a polygon are the angles at each vertex which are inside the polygon. There is one per vertex. So for a polygon with N sides, there are N vertices and N interior angles.
For a regular polygon, by the definition, all the interior angles are the same. In the figure drawn above, Click on "make regular" then change the number of sides and resize polygon by dragging any vertex. For any given number of sides, all the interior angles are same.
For irregular polygon , each and every angle can be different.
The interior angles of any polygon add up always to a constant value, which depends only on number of sides. For instance the interior angles of a pentagon add up always to 540° no matter if it irregular or regular, convex or concave, or what size and shape it has. Sum of the interior angles of a polygon can be given by the formula written below
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Sum = 180(n-2) degree
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where
n is number of sides
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For the regular polygon, the total described above is evenly spread among all the interior angles, as they all have same values. There are a number of polygons ... each having angles and sides. When we talk about angles of the polygon, we mean the interior angles usually. A polygon has the same number of interior angles as sides. The equilateral triangle has 3 equal 60 degree angles. The sum of the angles of any triangle is 180 degrees. The sum of 4 interior angles of a square is 360 degrees, which is same for any quadrilateral. The sum of interior angles increases by 180 ° for each additional side ... pentagon, hexagon, heptagon, octagon ... as polygons have more sides, interior angles become larger and there are more of them, hence the sum of interior angles increases. The sum of exterior angles of a polygon is 360º. To find measure of each exterior angle of the regular polygon, just divide 360 degrees by number of sides.
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