Question

If the sum of the interior angle of a polygon is $2340^\circ $, then find the number of sides of the polygon.

Answer 1

Hint:
To solve this, you have to know that the sum of the interior angle of a polygon is equal to $180(n - 2)$, where n is the number of sides. Then it's just basic algebra to solve.

Complete step by step solution:
Whatever the number of sides of a polygon, the sum of its exterior angles is always $360^\circ $
Further, each pair of exterior angle and interior angle add up to $180^\circ $
Hence, in a polygon with S sides (or angle),
The sum of all the interior and exterior angles would be $180^\circ \times S$
Formula,
And sum of interior angle would be, $180^\circ \times n - 360^\circ (S - 2)$
As sum of angle is $2340^\circ $
Hence, $180(S - 2) = 2340$
Or $S - 2 = \dfrac{{2340}}{{180}} = 13$
And $S = 13 + 2 = 15$
Polygon is a pentadecagon.

Note:
The number of sides is also the number of angles and , in a regular polygon, all the angles are the same. This is the basic property of a polygon.