Geometry - Show that x+y+z=360

• Oct 17th 2009, 02:44 PM
kevin3000
Geometry - Show that x+y+z=360
Ok. I've got a huge problem with this problem. Please use much text when you explain how to solve It so I understand.

http://i.imagehost.org/0952/K_4.jpg
• Oct 17th 2009, 03:16 PM
mr fantastic
Quote:

Originally Posted by kevin3000
Ok. I've got a huge problem with this problem. Please use much text when you explain how to solve It so I understand.

http://i.imagehost.org/0952/K_4.jpg

$x = 180^0 - a$ etc.

and then use $a + b + c = 180^0$.
• Oct 17th 2009, 03:19 PM
Plato
Using the exterior angle theorem $\left\{ \begin{gathered} x = b + c \hfill \\ y = a + b \hfill \\ z = a + c \hfill \\ \end{gathered} \right.$.

Note that $a+b+c=180$
• Oct 17th 2009, 03:36 PM
Matt Westwood
Interestingly, the sum of the exterior angles of ANY polygon is also 360 degrees. Thinking informally, this is clear if you imagine rotating a pin aligned along one side so it aligns against the next side. To do that, you rotate it through the exterior angle. By the time you've done this for all exterior angles, you're back where you started and your pin has rotated through 360 degrees.
• Oct 18th 2009, 03:59 AM
HallsofIvy
Just to throw my oar in, x and a, z and b, y and c each form a straight line so x+a= 180, z+ b= 180, and y+ c= 180. Adding those three equations, x+ a+ z+ b+ y+ c= 180+ 180+ 180= 540. but a+ b+ c= 180 because they are the interior angles in a triangle. 180+ x+ y+ z= 540 so x+ y+ z= 540-180= 360.