Question

The sum of the measures of the interior angles is 1449°. How many sides does the polygon have?

Answer 1

The sum of the measures of the interior angles is, S = 1440.

The total sum of interior angles of a polygon might be related to its number of sides by the following formula:

`S=(n-2)*180`

Here, S is the total sum and n is the number of sides.

Therefore, the number of sides can be calculated as,

`n=(S)/(180)+2`

Substituting for S, we get,

`n=(1440)/(180)+2=8+2=10`

Thus, the number of sides is 10.