Question 821913
Two angles of a triangle have measures of 55 degrees and 65 degrees . What could not be a measure of an exterior angle of the triangle ?
<pre>
Two of the angles are given as 55° and 65°.  We can find the third
angle by adding them and subtracting from 180°.

55°+65°=120°, 180°-120°=60°, so the third angle is 60°

{{{drawing(200,325/2,-3, 13,-3,11, line(-3,0,10,0), line(0,0,10,14.28148007),
line(6.002558223,8.572541562,12,-4.289014), locate(1,1.5,"55°"),
locate(7.4,1.5,"65°"), locate(4.7,7,"60°")


 )}}}

Now we find the three exterior angles, by subtracting each interior
angle from 180°:

180°-55°=125°,  180°-65°=115°,  180°-60°=120°

{{{drawing(200,325/2,-3, 13,-3,11, line(-3,0,10,0), line(0,0,10,14.28148007),
line(6.002558223,8.572541562,12,-4.289014), locate(1,1.5,"55°"),
locate(7.4,1.5,"65°"), locate(4.7,7,"60°"),locate(-2,1.5,"125°"),
locate(7.4,-.2,"115°"),  locate(6.35,8.8,"120°")


 )}}}


So the ONLY possible values for the exterior angles are 125°, 115°, 120°.

Any value other than 125°, 115°, 120° could not be the measure of an
exterior angle.

Edwin</pre>