Set up equations that represent the information you are given.
What is the sum of the angles within a triangle?
How can you use this to find ∠B?
One you know m∠B, solve for angles A and C.
m∠A = 3m∠B + 5°
m∠C = m∠B − 20°
m∠A + m∠B + m∠C = 180°
(3m∠B + 5°) + m∠B + (m∠B − 20°) = 180°
Solve for B.