Sum of Interior Angles of A Polygon
Sum of Interior Angles of A Polygon
Sum of Interior Angles of A Polygon
C D C D
When we divide quadrilateral ABCD along diagonal AC,
two triangles, △ABC and △ACD are formed.
Hence, we have:
Sum of the interior angles of quadrilateral ABCD
= sum of the interior angles of two triangles
= 2 180 Angle sum of a triangle = 180
= 360
Using a similar approach, we can
find the sum of the interior angles of
other polygons.
For examples,
A
2
B
No. of sides = 4
No. of triangle formed = 2
C D
Sum of interior angles = 2180 = 360
Quadrilateral
A
2
No. of sides = 5
B
E No. of triangle formed = 3
C D
Sum of interior angles = 3180 = 540
Pentagon
A 2
F No. of sides = 6
B No. of triangle formed = 4
E
Sum of interior angles = 4180 = 720
C D
Hexagon
From the above examples, let
us deduce the following for an
n-sided polygon.
For example,
sum of all the interior angles of a 12-sided polygon
= (12 2) 180 (∠ sum of n = 12
polygon)
= 1800
Follow-up question
1. Find x in the figure. A
Solution 93
B
93 + 121 + 82 + 138 + x = (5 2) 180 121 x E
(∠ sum of polygon) 138
82
434 + x = 540 D
C
x = 106
Follow-up question
2. For a regular octagon, find
(a) the sum of all the interior angles,
(b) the size of each interior angle.
Solution
(a) Sum of all the interior angles = (8 2) 180
(∠ sum of polygon)
= 1080
1080
(b) Size of each interior angle = A regular polygon is a
8 polygon with all sides
= 135 and all interior angles
equal.