Question 332812
It is possible for the interior angles of a triangle to be in the ratio 1:2:6,
<pre><b>
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°


{{{drawing(400,200,-.2,1.7,-.5,.5,

triangle(0,0,cos(20*pi/180),sin(20*pi/180),cos(20*pi/180)+sin(20*pi/180)/tan(40*pi/180),0),locate(.2,.08,"20°"), locate(1.14,.08,"40°"),
locate(.84,.3,"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</pre>