What is the sum of the interior angle measure of a 15-sided polygon?

Question

a_clan · Answer

180×(n-2)
here n=15

anonymous · Answer

where are you getting your answer from?

anonymous · Answer

Here's one way to get an answer: http://www.mathsteacher.com.au/year8/ch10_geomcons/02_internal/anglesum.htm

anonymous · Answer

Let's try to derive this formula!

anonymous · Answer

I think that the math teacher link is using induction to get to this generalization.

amistre64 · Answer

a 15-gon takes a circle and divides it 15 times; with central angles of 24.

Each segment then forms atriangle with a top angle of 24 and 2 equal base angles of (180 - 24)/2:   78

but then 2 base angles form the interior angle of each point so we could have just have left it at 180-24:  156

now with 15 points as well; that adds up to 15(156) i believe

anonymous · Answer

Hey, it would be great if you could upload a figure.

anonymous · Answer

i dont have a figure its only a question.

amistre64 · Answer

attachment

anonymous · Answer

the computer told me that the right answer is 2340

amistre64 · Answer

15(156) = 2340  yes

anonymous · Answer

The formula comes from the idea of dividing a polygon into triangles. A square (4-sided polygon) can be divided into 2 triangles by drawing a single diagonal. A pentagon can be divided into 3 triangles by choosing one vertex at random and then drawing lines out to each other vertex.

By doing this, one can show that an n sided polygon can be divided down into n-2 triangles. Since there are 180 degrees in any triangle, this provides a total of (n-2)(180) for the amount of degrees.