Triangle with Two 60-Degree Angles?

In the GeoGebra app below:

Construct a triangle with two 60-degree angles. Use A and B as points when using the ANGLE WITH GIVEN SIZE tool Toolbar Image.

Keep going: More directions appear below this applet.

Use the ANGLE tool Toolbar Image to measure this triangle's third angle. What is it? Does this result surprise you? Why should this third angle measure what it does?

8. Use the DISTANCE or LENGTH tool Toolbar Image to measure the lengths of the 3 sides of this triangle. Then select the MOVE tool Toolbar Image to move the vertices of this triangle around. What do you notice about any triangle that's equiangular?