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Polygons

Angles

In a polygon, the line running between non-adjacent points is known as a diagonal. The diagonals drawn from a single vertex to the remaining vertices in an n-sided polygon will divide the figure into n-2 triangles. The sum of the interior angles of a convex polygon is then just (n-2)* 180.

If the side of a polygon is extended past the intersecting adjacent side, it defines the exterior angle of the vertex. Each vertex of a convex polygon has two possible exterior angles, defined by the continuation of each of the sides. These two angles are congruent, however, so the exterior angle of a polygon is defined as one of the two angles. The sum of the exterior angles of any convex polygon is equal to 360°.

Kristin Lewotsky

KEY TERMS

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Angle: —A geometric figure created by two lines drawn from the same point.
Concave: —A polygon whose at least one angle is larger than the straight angle (180°).
Convex: —A polygon whose all angles are less than the straight angle (180°).
Diagonal: —The line which links-connects any two non-adjacent vertices.
Equiangular: —A polygon is equiangular if all of its angles are identical.
Equilateral: —A polygon is equilateral if all the sides are equal in length.
Parallelogram: —A rectangle with both pair of sides parallel.
Perimeter: —The sum of the length of all sides.
Rectangle: —A parallelogram in which all angles are right angles.
Reflex polygon: —A polygon in which two non-adjacent sides intersect.
Regular polygon: —An equilateral, equiangular polygon.
Rhombus: —A parallelogram whose adjacent sides are equal.
Square: —A four-sided shape whose sides are equal.
Vertex: —The point at which the two sides of an angle meet.

Additional topics

Science EncyclopediaScience & Philosophy: Planck mass to PositPolygons - Classification, Angles