IFFY Triangles

An arithmetic progression is where the terms of a sequence are increasing (or decreasing) by the same amount each time.  Here are two examples:

• $50, 60, 70$
• $66, 62, 58$

In the first case the numbers are increasing by $10$ each time and in the second they are decreasing by $4$ each time.  Only one of the two sets of numbers above can represent the angles in a triangle.

For the second pair of problems, a diagram might be useful.  You might find it helpful to add an extra line to your diagram and to think about congruent triangles.  Be careful that you don't assume things that need to be proved!