let a<b<c
c=75+a and (a+c)/3=b
using c from the first in the second you have:
b=(a+75+a)/3
b=(2a+75)/3
Since this is a triangle, a+b+c=180, using b and c from above we get:
a+(2a+75)/3+75+a=180 making the left side have a common denominator 3
(3a+2a+75+225+3a)/3=180 combine like terms on left side
(8a+300)/3=180 multiply both sides by 3
8a+300=540 subtract 300 from both sides
8a=240 divide both sides by 8
a=30°, since b=(2a+75)/3
b=45°, since c=75+a
c=105°
So the angles are 30°, 45°, and 105°
