Question

What is the sum of all interior angles of a regular
(i) pentagon
(ii) hexagon
(iii) nonagon
(iv) polygon of 12 sides?

Answer 1

Sum of the interior angles of an n-sided polygon = $\left(n-2\right)\times 180°$

(i) For a pentagon:
$$\begin{gathered} n=5 \\ \therefore \left(n-2\right)\times 180°=\left(5-2\right)\times 180°=3\times 180°=540° \end{gathered}$$

(ii) For a hexagon:
$$\begin{gathered} n=6 \\ \therefore \left(n-2\right)\times 180°=\left(6-2\right)\times 180°=4\times 180°=720° \end{gathered}$$

(iii) For a nonagon:
$$\begin{gathered} n=9 \\ \therefore \left(n-2\right)\times 180°=\left(9-2\right)\times 180°=7\times 180°=1260° \end{gathered}$$

(iv) For a polygon of 12 sides:
$$\begin{gathered} n=12 \\ \therefore \left(n-2\right)\times 180°=\left(12-2\right)\times 180°=10\times 180°=1800° \end{gathered}$$