Question

How many sides are in a polygon whose sum of the interior angles is 1440?

Answer 1

There are 10 sides.

Explanation:

If you draw triangles inside a polygon using one vertex and joining it to all the other vertices (without line crossing) the number of triangles will be 2 less than the number of sides . Hence `(n-2)` in the formula. Each triangle has 180°.

`1440 div 180` will give the number of triangles.

Then add 2 to find the number of sides.

`1441 div 180 = 8`triangles

`8+2 = 10 " sides"`

Or you could use the formula, it does exactly the same process.

`180(n-2) = 1440`

`n-2 = 1440/18 = 8`

`n = 8+2 = 10`