how many sides does a regular polygon have if one of the exterior angles=9°?
The sum of the exterior angles of a polygon is 360° and since there are n
exterior angles all with the same measure,
360°/n = 9°
Multiply both sides by n
360° = 5°n
Divide both sides by 5°
72 = n
That's the answer.
[Incidentally, a 72-sided regular polygon would be hard to tell
from a circle, unless it were very large.]
and
how many sides does a regular polygon have if one of the exterior angles=11.25°?
360°/n = 11.25°
Multiply both sides by n
360° = 11.25°n
Divide both sides by 11.25°
32 = n
Answer: 32 sides. Here's how a 32-sided regular polygon looks.
The green lines are drawn from the center to the vertices, and
would all be radii of a circumscribing circle:
Edwin