An interior angle of a regular convex polygon is 140°. How many sides does the polygon have?

Answer 1

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.

Answer 2

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

Answer 3

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.