I) Introduction
A polygon is a closed two-dimensional shape bounded by straight
lines.
Ex of polygons include triangles, quadrilaterals, pentagons &
hexagons.
A regular polygon is distinctive in that all sides are of equal length
and all its angles are of equal size.
Ex regular hexagon, regular pentagon, regular quadrilateral
( square), regular triangle ( equilateral triangle)
The name of each polygon is derived from the number of angles it contains.
3 angles
=
Triangle
7 angles
=
Heptagon
4 angles
=
Tetragon (quadrilateral)
8 angles
=
Octagon
5 angles
=
Pentagon
9 angles
=
Nonagon
6 angles
=
Hexagon
10 angles
=
Decagon
12 angles
=
Dodecagon
II) The sum of the interior angles of a polygon
The sum of the interior angle of a triangle is 180°
The sum of the interior angle of a quadrilateral is 360°. What about the other polygons ?
In the polygons below a straight line is drawn from each vertex to vertex A.
As can be seen, the number of triangles is always two less than the number of sides the polygon has, i.e. if
there are n sides, there will be (n - 2) triangles. Since the angles of a triangle add up to 180°
the sum of the interior angles of a polygon is therefore 180(n 2) degrees.
Ex : Find the sum of the interior angles of a regular pentagon and hence the size of each interior angle. For
a pentagon n = 5. So the sum of the interior angles = 180(5 - 2)'
= 180 x 30 = 5400
For a regular pentagon the interior angles are of equal size. So each angle
5
5400
108°.
III) The sum of the exterior angles of a polygon
The angles marked a, b, c, d, e and f (left) represent the
exterior angles of the regular hexagon drawn.
For any convex polygon the sum of the exterior angles is
360°
If the polygon is regular and has n sides, then each exterior
angle is
n
360
Ex :
a) Find the size of an exterior angle of a regular nonagon. (360 9 = 40°)
b) Calculate the nb of sides a regular polygon has if each exterior angle is 15°? (n = 360 15 = 24)
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