Answer:
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
