An interior angle of a regular convex polygon is 140°. How many sides does the polygon have?
sorry - you were using exterior angles.
If each interior angle is 140°, then if there are n sides,
180(n-2)/n = 140
n = 9
I apologize for the incorrect response. You are correct.
Using the formula for the sum of interior angles in a polygon,
180(n-2)/n = 140
We can simplify the equation by multiplying both sides by n:
180n - 360 = 140n
Subtracting 140n from both sides and adding 360 to both sides:
180n - 140n = 360
40n = 360
Dividing both sides by 40:
n = 9
Therefore, the polygon has 9 sides.
To find the number of sides a polygon has based on its interior angle, we can use the formula:
n = 360° / interior angle
Substituting in the given interior angle:
n = 360° / 140°
n ≈ 2.57
Since the number of sides of a polygon must be a whole number, we round 2.57 up to the next whole number, which is 3.
Therefore, the polygon has 3 sides.