Im stuck on this question please help?

Question

Caulculate the number of sides for a polygon whose interior angles add up to 1980

Answer 1

Let's figure out the formula....
A 3-side figure has 180 deg.
A 4-side figure has 360 deg.
A 5-side figure has 540 deg.
A 6-side figure has 720 deg.

So the formula is (n - 2) * 180 where n is the number of sides.
Work backwards:
1980 = 180n - 360
1620 = 180n
9 = n

Answer 2

Exterior angles always add up to 360°.

Let n be the amount of sides. Let x be the total of interior angles for one side:

360/n = x

Let Y be the total of all interior angles:

(180 - x) * n = Y

rearring this we get:

Y = (180 - 360/n) * n

Y = 180n * ( (n-2)/n)

Y = 180 * (n -2)

This is the general rule.

For a triangle we get: (n=3)
180°

For a square we get: (n=4)
360°

Now we just have to substitute in your values for the question:

Y = 180 * (n-2)

1980 = 180 * (n-2)

11 = n - 2

n = 13



I hope this helped. Please don't forget to select my answer as the best answer! Thank you.

Answer 3

Wow, that is a nifty question. I have never encountered that particular one.

We could start by what we do know. The interior angles of a triangle add up to 180 degrees.

The interior angles of a four-sided polygon add up to 360 degrees.

So the amount of degrees goes up rather quickly.

Doing this in my head, I would say that an octagon interior angles would be (90+180)/2 times eight. See where that leads you.

Answer 4

3 sides = 180
4 sides = 360
5 sides = 540

n sides = (n-2)*180

1980 = (n-2)*180

Go for it.

Answer 5

What he said..