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:

$S=(n-2)\times180$

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

Therefore, the number of sides can be calculated as,

$n=\frac{S}{180}+2$

Substituting for S, we get,

$n=\frac{1440}{180}+2=8+2=10$

Thus, the number of sides is 10.