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Question:

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 n number of sides?

Solution:

As per above table, convex polygon with 4 sides have angle sum (4-2) × 180° = 360°.
(a) (7-2) × 180° = 900° is the angle sum of convex polygon with 7 sides.
(b) (8-2) × 180° = 1080° is the angle sum of convex polygon with 8 sides.
(c) (10-2) × 180° = 1440° is the angle sum of convex polygon with 10 sides.
(d) For n sides (n-2) × 180° is the angle sum of convex polygon with n sides.