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

$s = 15$



EXPLANATION

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

$(s - 2) \times 180$

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




This implies that;

$(s - 2) \times 180 = 2340$

Dividing through by 180, we get,

$(s - 2) = \frac{2340}{180}$


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.