4. Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)


What can you say about the angle sum of a convex polygon with number of sides?

(a) 7

(b) 8

(c) 10

(d) n

From the given table, dearly we observe that the sum of angles (interior angles) of a polygon with n sides = \((n – 2)× 180^{\circ}\).
(a) n = 7

Sum of angle =\(\left( 7-2 \right) \times { 180 }^{ \circ }\)

\(= 5\times { 180 }^{ \circ }={ 900 }^{ \circ }\)

∴The sum of angle for 7 sided polygon=\(900^o\)

(b) n = 8

Sum of angles =\( \left( 8-2 \right) \times { 180 }^{ \circ }\) \(= 6\times { 180 }^{ \circ }={ 1080 }^{ \circ }\)

∴ The sum of the angles of a polygon of 8 sides=\(1080^o\)

(c) n = 10

Angle sum = \(\left( 10-2 \right) \times { 180 }^{ \circ }\)

\(= 8\times { 180 }^{ \circ }={ 1440 }^{ \circ }\)

∴ The sum of the angles of a polygon of 10 sides=\(1440^o\)

(d) We can observe from the given table that the number of triangles is two less them the number of sides in the polygon.

∴ If the polygon has n sides, the number of triangles formed will be (n – 2).

Also we know that the sum of angles of a triangle = \(180^{ \circ }\)

∴ The sum of angles of a polygon of n sides =\( (n – 2) \times180^{ \circ }\)