Question

To calculate the sum of the interior angles of a polygon multiply the number of sides by 180° This is true isn't it?

Answer 1

@ChristopherToni

Answer 2

It involves the number of sides, but it's not exactly \(180\cdot n\). For instance, when n=3 (a triangle), what should the angles add up to?

Answer 3

90?

Answer 4

Oh nevermind, it would be 180.

Answer 5

No. :-/

In a triangle, the sum the three angles should be 180 degrees. So if we want to plug n=3 into a formula, we would expect it to return 180. However, if the equation was \(180\cdot n\), then \(180\cdot 3=540\neq 180\). What this suggests is that we need to subtract something from n first and then multiply by 180.

The formula we're after should look something like \(180\cdot(n-x)\). In the case of a triangle, we want to find x so that \(180\cdot (3-x) = 180\). What do you get when you solve for x? :-)

Answer 6

(Sorry, didn't notice your correction there)

Answer 7

So my initial answer would be false?

Answer 8

What was your initial answer again?

Answer 9

I thought it to be true,,

Answer 10

Yes, your initial answer is incorrect. :-/

Answer 11

;-; I hate math. It's my worst subject, but yet, Biology is my best.

Answer 12

If you follow through with the triangle case, you see that \(x=2\). So it then follows for general n that the total sum of the interior angles of an n-gon is \(180\cdot (n\color{red}{-2})\).

Does this make sense? :-)