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

Question

Autumn Armstrong · Accepted Answer

#s=15#

Regardless of how many sides a polygon has,

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.

Noah Atkinson · Answer

undefined To find the number of sides of a polygon given the sum of its interior angles, you can use the formula:

$$ \text{Sum of interior angles} = (n - 2) \times 180^\circ $$

Where $ n $ is the number of sides of the polygon.

Given that the sum of all the interior angles of the polygon is $ 2340^\circ $, we can set up the equation:

$$ 2340^\circ = (n - 2) \times 180^\circ $$

Now, solve for $ n $:

$$ (n - 2) \times 180^\circ = 2340^\circ $$

$$ n - 2 = \frac{2340^\circ}{180^\circ} $$

$$ n - 2 = 13 $$

$$ n = 13 + 2 $$

$$ n = 15 $$

So, the polygon has 15 sides.