Question

The sum of the angles of a polygon is 10800. Then how many sides does it have?​

Answer 1

Answer:

Explanation:

Recall that the formula for the sum of the interior angles in a regular polygon is:

∣

∣

∣

∣

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

a

a

180

∘

(

n

−

2

)

a

a

∣

∣

−−−−−−−−−−−−−−−

where

−−−−− :

n

=

number of sides

In your case, since the sum of the interior angles is

720

∘

, then the formula must equal to

720

∘

. Hence,

720

∘

=

180

∘

(

n

−

2

)

Since you are looking for

n

, the number of sides the polygon has, you must solve for

n

. Thus,

720

∘

180

∘

=

n

−

2

4

=

n

−

2

n

=

∣

∣

∣

∣

¯¯¯¯¯¯¯¯¯¯¯

a

a

6

a

a

∣

∣

−−−−−−

Since

n

=

6

, then the polygon has

6

sides.