I’m a regular polygon each interior angle is greater than each exterior angle by 90 degrees. Calculate the number of sides in the polygon.

Let the number of sides of the regular polygon be \( n \).

The formula for the interior angle \( I \) of a regular polygon with \( n \) sides is given by:

\[
I = \frac{(n-2) \times 180}{n}
\]

The formula for the exterior angle \( E \) of a regular polygon is:

\[
E = \frac{360}{n}
\]

According to the problem, each interior angle is greater than each exterior angle by 90 degrees:

\[
I = E + 90
\]

Substituting the formulas for the interior and exterior angles into this equation gives:

\[
\frac{(n-2) \times 180}{n} = \frac{360}{n} + 90
\]

To eliminate the fractions, multiply both sides by \( n \):

\[
(n-2) \times 180 = 360 + 90n
\]

Expanding the left-hand side:

\[
180n - 360 = 360 + 90n
\]

Now, let's isolate \( n \):

\[
180n - 90n = 360 + 360
\]

This simplifies to:

\[
90n = 720
\]

Dividing both sides by 90 gives:

\[
n = 8
\]

Thus, the polygon is an octagon (a regular polygon with 8 sides).

To verify, we can calculate the interior and exterior angles for \( n = 8 \):

1. Calculate the interior angle:

\[
I = \frac{(8-2) \times 180}{8} = \frac{6 \times 180}{8} = \frac{1080}{8} = 135 \text{ degrees}
\]

2. Calculate the exterior angle:

\[
E = \frac{360}{8} = 45 \text{ degrees}
\]

Now check the relationship:

\[
I - E = 135 - 45 = 90 \text{ degrees}
\]

This confirms our solution is correct. Therefore, the number of sides in the polygon is

\[
\boxed{8}
\]