Math, asked by mist32, 7 months ago

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

Answers

Answered by guptagauri727
0

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.

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