Prove Quadrilateral Exterior Angles Equal Interior Angles

[msimard8]

Hmmm I seem to be stumped on this question.

Prove that the sum of the exterior angles at opposite verticies of any quadrilateral is equal to the sum of the interior angles at the other two verticies?

I don't really have a start because I can't seem to get my mind wrapped around where to begin.

I know the sum of exterior angles is 360 degrees. And the sum of interior angles in a quadilateral is equal to 360 degrees aswell.

I don't know where to go from there.

Hint or Help please
thanks

 

[0rthodontist]

Let the four interior angles be a, b, c, d, as in this picture

You know the sum of the interior angles is 360 degrees. So a + b + c + d = 360

Now you want to know what a + b equals. What does it equal? Can you rewrite that in terms of the exterior angles of c and d? (What exactly are those exterior angles?)

 

[msimard8]

thanks for the help

problem solved