The Exterior Angle Theorem on a Sphere

Below is an applet showing the setup for the (neutral) proof of the Exterior Angle Theorem, redrawn on a sphere. The theorem holds in the configuration shown, but you can move the triangle around so that the theorem fails.
3d graphics work best if you first right-click on the background and select "Zoom to fit".
(You can resize the image afterward if desired using your scroll wheel or by selecting Zoom from the right-click menu.)
Shift-click while using the mouse to move the viewing window.