Question

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

Figure
Side	3	4	5	6
Angle sum	180°	2 × 180° = (4 − 2) × 180°	3 × 180° = (5 − 2) × 180°	4 × 180° = (6 − 2) × 180°

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

(a) 7

(b) 8

(c) 10

(d) n

Answer 1

From the table, it can be observed that the angle sum of a convex polygon of n sides is,

(n −2) × 180º.

Hence, the angle sum of the convex polygons having number of sides as above will be as follows.

(a) If number of side $n=7$

(n −2) × 180º.

(7 −2) × 180º = 900°

(b) If number of sides $n=8$

(n −2) × 180º.

(8 −2) × 180º = 1080°

(c)If number of sides $n=10$

(n −2) × 180º.

(10 −2) × 180º = 1440°

(d) If number of sides $n=n$

(n −2) × 180º.

(n− 2) × 180°