ANGLES IN A POLYGON
A polygon is any plane shape with straight lines.
Examples are;
Triangle
3sides
1
Quadrilateral
4sides
2triangles
Pentagon
5sides
3triangles
Hexagon
6sides
4triangles
Heptagon
7sides
5triangles
Octagon
8sides
6triangles
Nonagon
9sides
7triangles
Decagon
10sides
8triangles
A regular polygon has all sides and all angles equal.
Formula for polygon
The sum of the angles of a polygon = (n – 2) x 180
or (2n – 4) x 90 or 0= (n – 2) x 2right angles or
2n – 4right angles
The interior angle of a polygon =
0
(n - 2) x 180
Number of triangles in a polygon = n – 2
n
Where n means number of side
Examples
1. The sum of the angles of a polygon is 12600. How many
sides has the polygon?
0
Solution
Sum of the angles of a polygon = (n – 2) x 180
1260 = 180n - 360
180n = 1260 + 360
180n = 1620
Divide both sides by 180
n=
n = 9sides
1620
180
2. Find the sum of the interior angles of a regular
heptagon.
Solution
Sum of the angles of a polygon = (n – 2) x 180
Heptagon (n) = 7
Sum of the angles of a polygon = (7 – 2) x 180
= 5 x 180
= 900
0
0
0
3. Calculate the size of each angle of a regular Octagon.
Solution
Sum of the angles of a polygon = (n – 2) x 1800
Octagon (n) = 8
= (n – 2) x 1800
= (8 – 2) x 180
= 6 x 180
= 10800
Each sizes =
1080
0
= 135
8
Class work
1. Find the sum of the interior angles of
heptagon.
2. Calculate the size of each angle of a regular 15
sided polygon.
3. Each of the interior angles of a regular
polygon is 1080. How many sides has the
polygon?