How do I find the number of sides a regular polygon has if I only know te measure of the exterior angle, such as 40 degrees?
Use the strategy I mentioned in your later question.
If the sum of the exterior angles of any polygon is 360, and one angle is 40, divide the sum by the measure of one angle.
360/40=9.
So, this particular polygon has 9 sides.
To find the number of sides in a regular polygon when you only know the measure of the exterior angle, you can use the formula:
n = 360° / x,
where n represents the number of sides and x represents the measure of the exterior angle.
In your case, the measure of the exterior angle is 40 degrees. Plugging this value into the formula, we get:
n = 360° / 40°.
Performing the division:
n = 9.
Therefore, the regular polygon has 9 sides.