Question

If sum of all the interior angles of a polygon is `2340^@`, how many sides does it have?

Answer 1

`s=15`

Explanation:

Whatever the number of sides of a polygon,

the sum of its exterior angles is always `360^@`

Further, each pair of exterior angle and interior angle adds up to `180^@`

Hence in a polygon with `s` sides (or angles),

the sum of all the interior and exterior angles would be `180^@xxs`

and sum of interior angles would be `180^@xxn-360^@=180^@(s-2)`

As sum of angles is `2340^@`

Hence, `180(s-2)=2340` or `s-2=2340/180=13`

and `s=13+2=15` and polygon is a Pentadecagon.