4. Calculate the measure of $\angle \mathrm{ABC}$, to the nearest degree.

Step 1 ：Let $x$ be the number of degrees in $\angle A$. Then $\angle C=4x^\circ$, and $\angle B$ is also $4x^\circ$ (since $\angle B$ is congruent to $\angle C$).

Step 2 ：Since the sum of angles in a triangle is $180^\circ$, we have $$x + 4x + 4x = 180,$$

Step 3 ：Solve for $x=20$. Therefore, $\angle B = 4\cdot 20 = \boxed{80}$ degrees.