If each angle of a regular polygon measures 140 degrees, how many sides does it have?
Are these external angles or internal angles?
I will assume that they are internal angles. That would make the external angles 40 degrees each. Since the external angles must add up to 360, the number of sides, and angles is 360/40 = 9.
http://www.coolmath.com/reference/polygons.html
To find the number of sides of a regular polygon, you can use the formula:
Number of sides = 360 degrees / Measure of each angle
In this case, the measure of each angle is 140 degrees, so plugging it into the formula:
Number of sides = 360 degrees / 140 degrees
Dividing 360 by 140, you get:
Number of sides ≈ 2.57
Since a polygon cannot have a fractional number of sides, you would round this number to the nearest whole number.
Thus, a regular polygon with each angle measuring 140 degrees has 3 sides, because rounding 2.57 to the nearest whole number gives 3.