Help! 7th grade advanced math question!?

Question

What is the sum, of the measures,of the angles of a 12 sided polygon. Hint: choose one vertice and create as many triangles as you can.

12 sided polygon http://etc.usf.edu/clipart/37300/37388/12-gon_37388_lg.gif

please help!

Answer 1

I will suggest another way of doing this problem. remember the sum of the exterior angles of any polygon no matter how many sides is 360.

So a regular polygon has each exterior angle equal to 360/n, n is he number of sides. (I know your polygon is not a regular polygon but bear with me none-the-less.)

If the polygon were regular each exterior angle would be 360/12 = 30. the interior angles would all be 180 - 30 = 150.

150*12 = 1800.

We can do it this way because the sum of the angles of a 12 sided polygon is ALWAYS the same.

Answer 2

i dunno about making triangles, but there is a simple formula that will do this for you.

180n-360=sum, where n is the number of sides

180(12)-360=1800

this is the sum, and if you want what every angle would be just divide that by twelve, or 150

make it a good day

Answer 3

I'm going to help you because you have your own teacher.

Answer 4

Thankfully, there is a formula for this.

The sum of the angles in any polygon with

n-sides is: (n-2)(180)

For a 12-sided polygon

(12-2)(180) = (10)(180) = 1800

1800 is the sum of all the angles.

Here is what your teacher is saying...

Take a square.

Draw a diagonal on the square.

This forms two triangles.

Each triangle's angles have a sum of 180 degrees

There are 2 triangles in the square, so the square's angles have a sum of 360 degrees.

This is why the formula given above works.

And if you're still reading, thanks for being patient and reading everything.

Answer 5

The sum of the interior angles for any regular polygon is 180*number_of_sides - 360

180*12-360 = 1800

Answer 6

The sum of the measures of the angles of a polygon

= (number of sides - 2) x 180

Since our figure has 12 sides

= (12 - 2) x 180

= 10 x 180

= 1800 degrees

Hope this helps you!  Please email anytime for further questions.

Answer 7

there is an easier way to think of this.

pretend that the sides are stretchy.

pick to verticies, and pull.

what you end up with is 2 angles of 0 degrees, and 10 of 180 degrees.

thus the formula  (n-2)*180