Final answer:
A regular polygon with interior angles measuring 168.75 degrees has 32 sides. This is determined by using the formula for the sum of interior angles of a polygon and solving for the number of sides (n).
Step-by-step explanation:
When a student asks about the number of sides a regular polygon with interior angles measuring 168.75 degrees has, we use the relationship between the number of sides (n) and the measure of each interior angle. For any regular polygon, the sum of the interior angles is given by 180(‑n−2) degrees, since a regular polygon can be divided into (n−2) triangles, each with a sum of angles equal to 180 degrees. Since we are given the measure of one interior angle, we can find n by rearranging the formula for the individual angle, which is (180(‑n−2)/n).
Setting the individual angle to 168.75 degrees and solving for n gives us:
168.75 = (180(‑n−2)/n)
Multiplying both sides by n and then expanding the equation, we have:
n*168.75 = 180‑*‑n−360
This simplifies to:
168.75n = 180n−360
Then:
360 = 180n−168.75n
360 = 11.25n
Finally:
n = 360 / 11.25
n = 32
Therefore, a regular polygon with interior angles measuring 168.75 degrees has 32 sides.