smc

Let $\angle A=x$ and $\angle B=y$. From the first condition, we have $x=4y$. From the second condition, we have $$90-y=4(90-x).$$ Substituting $x=4y$ into the previous equation and solving yields $$\begin{array}{rl}90-y=4(90-4y)& ⟹90-y=360-16y\\ & ⟹15y=270\\ & ⟹y=\boxed{18^{\circ }}\end{array}$$