Question

Is the sum of the angles of any polygon 1600?how about 900?

Answer 1

The sum the angles of any polygon is (n-2)*180°
Where n is no of vertices.
1600=(n-2)*180
1600/180=(n-1)
80/9=(n-1)
n=80/9+1
n=89/1
THEREFORE IT IS NOT POSSIBLE.
900=(n-2)*180
900/180=n-2
5=n-2
n=7
THEREFORE IT IS POSSIBLE.

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Answer 2

Step-by-step explanation:

If the sum of any polygon S=1600

1600=(n-2)×180

1600/180=(n-2)

8.8=(n-2)

n=8.8+2

n=10.8

the sum of n is in fraction so the sum of the angle of any polygon is not 1600°

If the sum of the angle of any polygon S=900°

900=(n-2)×180

900/180=n-2

5=(n-2)

n=5+2

n=7

the value of n is 7

so, yes the sum of the angle of any polygon is 900°