J4

n n-2
From the above table we see that:
For a polygon with n sides:
the sum of the interior angles is = (n – 2) × 180 0 .
Sum of exterior angles of a convex polygon.
A convex polygon has all its sides pointing outwards. The sum of the exterior angles of a
polygon is 360 0 .
A regular polygon has all its sides equal and all angles equal.
Example
(i)
(ii)
Solution
(i)
Find the sum of the interior angles of a pentagon
The sum of the interior angles of a polygon is 900 0 . How many sides has the
polygon?
The sum of the interior angles of a polygon with n sides is
(n – 2) × 180 0 . A pentagon has 5 sides. So the sum of the interior angles of a
pentagon is (5 – 2) × 180 0 = 3 × 180 0 = 540 0 .
(ii) 900 0 = (n – 2) × 180 0
n 2 5 + 2 = n
0
900
0
180
Therefore, n = 7. The polygon has 7 sides.
Example
Find the interior angle of a regular octagon.
Solution
Sum of interior angles of an octagon is
(8 – 2) × 180 0 = 6 × 180 0
= 1080 0 .
1080
Therefore, interior angle =
8
= 135 0 .
Alternative method:
360
Exterior angle of regular octagon = 8
= 45 0
Therefore, interior angle of regular octagon = 180 0 – 45 0 = 135 0 .
Example
Find the interior angle of a regular polygon with 9 sides.
Solution
The sum of all the 9 exterior angles = 360 0