Triangle Exterior Angles: Quick Exploration
In the GeoGebra app below,
1) Use the POLYGON 
tool to construct triangle ABC.
2) Select the RAY 
tool.
Construct a ray with endpoint A that passes through B.
Construct a ray with endpoint B that passes through C.
Construct a ray with endpoint C that passes through A.
3) Select the POINT ON OBJECT 
tool.
Plot a point D on ray AB that does not lie between A and B.
Plot a point E on ray BC that does not lie between B and C.
Plot a point F on ray CA that does not lie between C and A.
Keep going! More directions appear below this app.
tool to construct triangle ABC.
2) Select the RAY tool.
Construct a ray with endpoint A that passes through B.
Construct a ray with endpoint B that passes through C.
Construct a ray with endpoint C that passes through A.
3) Select the POINT ON OBJECT tool.
Plot a point D on ray AB that does not lie between A and B.
Plot a point E on ray BC that does not lie between B and C.
Plot a point F on ray CA that does not lie between C and A.
Keep going! More directions appear below this app. 4) Select the ANGLE 
tool. Then select points D, B, C (in that order). This is one exterior angle of this triangle.
5) Find and display the measures of the other 2 exterior angles of this triangle.
6) Go to the ALGEBRA view. Now calculate the sum of the measures of these 3 exterior angles.
tool. Then select points D, B, C (in that order). This is one exterior angle of this triangle.
5) Find and display the measures of the other 2 exterior angles of this triangle.
6) Go to the ALGEBRA view. Now calculate the sum of the measures of these 3 exterior angles. Select the MOVE 
tool. Move any one (or more) of the triangle's vertices around.
What can we conclude about the sum of the measures of the exterior angles of this triangle? Be specific in your response!