Yes it is possible.

Let the interior angles be 1x°, 2x° and 6x°

Since the sum of the three interior angles of a triangle is 180° 


1x° + 2x° + 6x° = 180°
          9x° = 180°
           x° = 20°

2x° = 40°

6x° = 120°  

Yes by having angles 20°, 40°, and 120°




but is it possible for the exterior angles of a triangle to be in the ratio 1:2:6? Why or why not?

No, so let's find out why:

Let the exterior angles be 1x°, 2x° and 6x°

Since the sum of the three exterior angles of a triangle is 360° 

1x° + 2x° + 6x° = 360°
          9x° = 360°
           x° = 40°

2x° = 80°

6x° = 240°  

No because an exterior angle of a triangle is the supplement
of an interior angle, and 240° is a reflex angle, too big to 
be the supplement of any angle.

Edwin