in angle ABC the measurement of the latgest angle is 32 less than 3 times the smallest angle the measurement of the middle angle

Answer 1

γ=3α-32

α=(γ+32)/3

β=180-α-γ

Answer 2

Let A be the largest angle and C = the smallest angle. Thus A = 3C-32. Note that ABC will form a triangle where the sum of the 3 angles must be = 180, thus A+B+C = 180. Note that there are three variables (A B C) and only two equations. The two can be combined 3C-32+B+C = 4C+B-32=180. Simplifying to B+4C= 148. Without a further limit on B or C we find that B can range from 0 to 148 yielding C to range from 0 to 37.