What is the sum of all interior angles of a regular

Question:

What is the sum of all interior angles of a regular

(i) pentagon

(ii) hexagon

(iii) nonagon

(iv) polygon of 12 sides?

Solution:

Sum of the interior angles of an $n$-sided polygon $=(n-2) \times 180^{\circ}$

(i) For a pentagon:

$n=5$ $\therefore(n-2) \times 180^{\circ}=(5-2) \times 180^{\circ}=3 \times 180^{\circ}=540^{\circ}$

(ii) For a hexagon:

$n=6$ $\therefore(n-2) \times 180^{\circ}=(6-2) \times 180^{\circ}=4 \times 180^{\circ}=720^{\circ}$

(iii) For a nonagon:

$n=9$ $\therefore(n-2) \times 180^{\circ}=(9-2) \times 180^{\circ}=7 \times 180^{\circ}=1260^{\circ}$

(iv) For a polygon of 12 sides:

$n=12

$\therefore(n-2) \times 180^{\circ}=(12-2) \times 180^{\circ}=10 \times 180^{\circ}=1800^{\circ}$

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