Question

is the sum of the angles of any polygon 1600° ? how about 900°?

Answer 1

The sum of the interior angles of a convex polygon is given by: (n-2)180 degs. n-2 = 5 Add 2 to both sides. n = 7 This is the number of sides in thepolygon the sum of whose interiorangles is 900 degrees.

Answer 2

Answer and Explanation :

To find : Is the sum of the angles of any polygon 1600° ?

Solution :

We know that,

Sum of angle in any polygon is given by,

$S=(n-2)\times 180$

We have given that, The sum of the angles of any polygon S=1600°

Substitute in the formula,

$1600=(n-2)\times 180$

$\frac{1600}{180}=(n-2)$

$8.8=(n-2)$

$n=8.8+2$

$n=10.8$

The value of n is in fraction so no the sum of the angles of any polygon is not 1600°.

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

Substitute in the formula,

$900=(n-2)\times 180$

$\frac{900}{180}=(n-2)$

$5=(n-2)$

$n=5+2$

$n=7$

The value of n is 7.

So, Yes the sum of the angles of any polygon is 900°.