Question

Which of the following formulas find the sum of interior angles a polygon with n number of sides?
A; 360n
B;180n-360
C; 180m
D; 180-180

WILL FAN AND MEDAL // I think its D but im not to sure

Answer 1

You think it's D....?
So you think the interior angles of a polygon will always add up to 180-180 degrees? :o

Answer 2

Then C cause interior angle formula basically equals 180 right ??

Answer 3

A triangle has 3 sides.
The interior angles of a triangle add up to 180 degrees.
\(\large\rm 180\cdot1\)
We have one of these 180 degrees for a triangle.
I want to rewrite this 1 in a clever way that involves the number of sides.
\(\large\rm 180\cdot(3-2)\)
1 can be rewritten as 3-2, now we have a setup that involves the number of sides (3).

How about a square?
A square has two triangles in it.
So a square has two of these 180 degrees for interior angles.
\(\large\rm 180\cdot2\)
Again, we want to rewrite this 2 as something related to the number of sides of a square.
\(\large\rm 180\cdot(4-2)\)

So if we generalize this,
we see that we're always multiplying 180 by `two less than` the number of sides (n).
\(\large\rm 180\cdot(n-2)\)

Answer 4

180(n-2) corresponds to one of your options,
you'll have to distribute the 180 to figure out which one.

Answer 5

A

Answer 6

180(n-2)
would distribute to
180n - 180(2)
180n-360