Question

The sum of the angle measures of a polygon with s sides is 2340. find s.

Answer 1

s=15

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∘×s

and sum of interior angles would be 180∘×n−360∘=180∘(s−2)

As sum of angles is 2340∘

Hence, 180(s−2)=2340 or s−2=2340180=13

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

i hope u understand :)

Answer 2

ANSWER


`s = 15`



Step-by-step explanation

The sum of angles in a regular polygon with s sides is given by


`(s - 2) * 180`

It was given that, the sum of the angle measures of a polygon is 2340.




This implies that;


`(s - 2) * 180 = 2340`

Dividing through by 180, we get,


`(s - 2) = (2340)/(180)`


Simplify the right hand side to get;


`(s - 2) = 13`

We make s the subject to obtain,


`s = 13 + 2`
Simplify to obtain;


`s = 15`


Therefore the polygon has 15 sides.