To find the sum of the interior angles of a convex polygon, you can use the formula:

$\text{Sum of interior angles} = 180^\circ \times (n - 2)$

where $n$ is the number of sides of the polygon.

For a 32-gon, $n = 32$, so the sum of the interior angles is:

$\text{Sum of interior angles} = 180^\circ \times (32 - 2) = 180^\circ \times 30 = 5400^\circ$

Thus, the sum of the interior angles of a convex 32-gon is $5400^\circ$.

Let me know if you'd like more details or if you have any questions!

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Here are some related questions to further your understanding:

1. How would the sum of the interior angles change for a convex 50-gon?
2. What is the measure of each interior angle of a regular 32-gon?
3. How does the formula for the sum of interior angles apply to polygons with fewer sides?
4. What is the relationship between the sum of interior angles and the exterior angles of a polygon?
5. Can a concave polygon have a sum of interior angles different from that of a convex polygon?

Tip: The sum of the exterior angles of any polygon, whether convex or concave, is always $360^\circ$.