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 $ 7 , 8 , 10 and n$?

\begin{tabular}{|l|c|c|c|c|} \hline Figure & 3 & 4 & 3 \\ \hline Side & \( 180^{\circ} \) & \( 2 \times 180^{\circ} \) \( =(4-2) \times 180^{\circ} \) & \( 3 \times 180^{\circ} \) \( =(5-2) \times 180^{\circ} \) & \( 4 \times 180^{\circ} \) \( =(6-2) \times 180^{\circ} \) \\ \hline Angle Sum & & \end{tabular}

Answer 1

Interior angle sum:

As per the given table the sum of the angles of a convex polygon with $4$sides is $(4–2)\times 180°=360°.$

For sides $7$

Therefore, $(7–2)\times 180°=5\times 180°=900°$is the angle sum of convex polygon with $7$ sides.

For sides $8$

Therefore, $(8–2)\times 180°=6\times 180°=1080°$is the angle sum of convex polygon with $8$ sides

For sides $10$

Therefore,$(10–2)\times 180°=8\times 180°=1440°$is the angle sum of convex polygon with $10$ sides

For sides $n$

Therefore,$(n–2)x180°$