Question

West High School has a math building in the shape of a regular polygon. When Mrs. Woods measures an interior angle of the polygon (which is inside her classroom), she gets 135°. How many sides does the math building have?

Answer 1

`8` sides
The math building is an octagon

Explanation:

The sum of all the interior angles in a polygon can be found by the equation `S=180(n-2)` where `n` is the number of sides the polygon has.

We know that one interior angle is `135` degrees and that all the interior angles are the same because this is a regular polygon. So the sum of the angles must be `135n` (`135` degrees times the number of sides, or the number of angles).

`135n=180(n-2)`

`135n=180n-360`

`135n+360=180n`

`45n=360`

`n=8 rarr` There are `8` sides and `8` interior angles of `135` degrees