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Angle measures in a polygon
A polygon is a closed plane (flat) figure with straight sides. There is a way to measure the sum of the interior angles that depends upon the number of sides (which is the same as the number of angles).
The interior angles of a polygon are those angles at each vertexthat are on the inside of 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 definition, all the interior angles are the same. In the figure above, Click on make regular then change the number of sides and resize the polygon by dragging any vertex. Notice that for any given number of sides, all the interior angles are the same.
For an irregular polygon , each angle may be different.
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 5400 no matter if it regular or irregular, convex or concave, or what size and shape it is. The sum of the interior angles of a polygon is given by the formula
sum=180(n-2)degree
Where n is the number of sides
For a regular polygon, the total described above is spread evenly among all the interior angles, since they all have the same values. There are many kinds of polygons ... each with angles and sides. When we talk about the angles of a polygon, we usually mean the interior angles. A polygon has as many interior angles as sides. An equilateral triangle has three equal 60 degree angles. The sum of the angles of this and any triangle is 180 degrees. The sum of the four interior angles of a square is 360 degrees, which is the same for any quadrilateral. The sum of the interior angles increases by 180 degrees for each additional side ... pentagon, hexagon, heptagon, octagon ... as the polygons have more sides, the interior angles become larger and there are more of them, so the sum of the interior angles increases. The sum of the exterior angles of a polygon is 3600. To find the measure of each exterior angle of a regular polygon, you just divide 360 degrees by the number of sides.
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