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 nsides is (n −2) × 180º. Hence, the angle sum of the convex polygons having number of sides as above will be as follows.

(a) (7 − 2) × 180º = 900°

(b) (8 − 2) × 180º = 1080°

(c) (10 − 2) × 180º = 1440°

(d) (n − 2) × 180°