Question

If the sum of all the angles of a polygon except one angle is 2220, then the number of sides of the polygonis

Answer 1

Please see the attachment

Answer 2

Answer:

Number of sides would be 15.

Step-by-step explanation:

Since, we know that the sum of all interior angles of a polygon with sides n is,

(n-2) × 180°,

Let after excluding x angle of a polygon, the sum of angles = 2220°

i.e. (n-2) × 180 - x = 2220

(n-2)× 180 = 2220 + x --------(X)

Now, n must be an positive integer greater than 3,

For this 2220 + x have to divisible by 180,

i.e. the value of x must be a number having 0 in ones place, such that 2220 + x is divisible by 180,

Possible values of x = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130........

When we check all these number,

We observed that,

The minimum value of x would be 120,

Because, $\frac{2220+120}{180}=\frac{1340}{180}=13=\text{ whole number}$

From equation (X),

(n-2)× 180 = 2220 + 120

n - 2 = 13

⇒ n = 15

Hence, the least number of sides of the polygon would be 15.