West High School has a math building in the shape of a regular octagon. When Mrs. Woods measures an interior angle of the octagon (which is inside her classroom), she gets 135°.
Mrs. Wood’s ceiling is 10.0 feet high and the length of one side of the building is 25.0 feet. What is the volume of West High School’s math building?

8 sides

The building is an octagon

Step-by-step 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

135

n

(

135

degrees times the number of sides, or the number of angles).

135

n

=

180

(

n

−

2

)

135

n

=

180

n

−

360

135

n

+

360

=

180

n

45

n

=

360

n

=

8

→

There are

8

sides and

8

interior angles of

135

degrees