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 number of sides?
(a) $7$ (b) $8$ (c) $10$ (d) $n$

Answer 1

As per above table, convex polygon with $4$ sides have angle sum $(4-2)\times {180}^o$

(a)

$(7-2)\times {180}^o={900}^o$ is the angle sum of convex polygon with $7$ sides

(b)

$(8-2)\times {180}^o={1080}^o$ is the angle sum of convex polygon with $8$ sides

(c)

$(10-2)\times {180}^o={1440}^o$ is the angle sum of convex polygon with $10$ sides

(d) For $n$ sides

$(n-2)\times {180}^o$ is the angle sum of convex polygon with $n$ sides