You have the following expressions for angles ∠A and ∠B:
∠A = 2x + 30
∠B = 3x - 20
In order to find the measure of angle ∠B it is necessary to solve for x.
You consider that angle ∠A and the angle just above the line are supplementary, that is, they add up 180°.
Furthermore, you consider that angle above angle ∠A is equal to angle ∠B, because the lines which cross the secant line are parallel.
Thus, what you have is that the sum of angles ∠A and ∠B is equal to 180°.
∠A + ∠B = 180 you replace by the algebraic expressions
2x + 30 + 3x - 20 = 180 simplify similar terms left side
2x + 3x + 30 - 20 = 180
5x + 10 = 180 subtract 10 both sides
5x = 180 - 10
5x = 170 divide by 5 both sides
x = 170/5
x = 34
Next, you replace the previoues value of x into the expression for angle ∠B:
∠B = 3x - 20 = 3(34) - 20 = 102 - 20 = 84
Hence, the measure of angle ∠B is 84°