Question

Find the sum of the interior angles of a polygon with 16 sides.​

Answer 1

Answer:

2520

Step-by-step 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

n

sides (or angles),

the sum of all the interior and exterior angles would be

180

∘

×

n

and sum of interior angles would be

180

∘

×

n

−

360

∘

=

180

∘

(

n

−

2

)

Hence sum of interior angles of a convex 16-sided polygon would be

180

∘

×

(

16

−

2

)

=

180

∘

×

14

=

2520

∘

.