what is the equation to find one interior angle of a polygon?

Question

mertsj · Answer

number of sides -2
Multiply that by 180
Divide that by the number of sides.

anonymous · Answer

We are assuming this is a regular polygon, thus all angles equal.

anonymous · Answer

yes they are thank you . so for an octagon it would be 8-2/180

mertsj · Answer

Yes.  it would be 8-2 times 180 and then divide that answer by 8

anonymous · Answer

Neat.

anonymous · Answer

so to be sure it is (8-2)/180=x/8

mertsj · Answer

If you have an octagon, you can divide it into 6 triangles
The sum of the angles of 6 triangles is 6 times 180 which is 1080
A regular octagon has 8 congruent angles.  1080 divided by 8 means there must be 135 degrees in each angle of the octagon.  So the answer is 135 degrees.

mertsj · Answer

Because there are 8-2 triangles which is 6 triangles.  In 6 triangles there are 6(180) degrees.
6(180)=1080
Divide that by 8 because there are 8 angles.  1080/8=135 so the answer is 135 degrees in each interior angle of a regular octagon.

mertsj · Answer

That leads us to the formula which says to subtract 2 from the number of sides.  
8-2=6
Then the formula says to multiply that by 180
6(180)=1080
Then the formula says to divide that by 8 because an octagon has 8 angles.
1080/8=135.  So the answer is 135

mertsj · Answer

$$Degrees \frac{(n-2)(180)}{n}$$

mertsj · Answer

See, in the formula n = the number of sides so that would be:
$$degrees = \frac{(8-2)(180)}{8}$$
$$degrees = \frac{6(180)}{8}$$
$$degrees = \frac{1080}{8}$$
$$degrees = 135$$

mertsj · Answer

And that is the answer.  Each of the interior angles of a regular octagon has a measure of 135 degrees.

anonymous · Answer

thanks thatt helped lots