I am going to let A be the measure of angle a, B be the measure of angle b and C be the measure of angle c, all in degrees. The statement
angle a is four times as large as angle b
A = 4 B
and the statement
angle c measures 20 degrees less than angle b
C = B - 20
In any triangle the sum of the measures of the angles is 180 degrees and hence
A + B + C = (4 B) + B + (B - 20) = 180
Solve for B.
Once you know B you can find A and C.