1. **State the problem:** We are given a right triangle with angle $\angle A = 30^\circ$, side $AC = 18$ units (adjacent to $\angle A$), and we need to find the measure of $\angle B$. 2. **Recall the triangle angle sum rule:** The sum of angles in any triangle is $180^\circ$. Since this is a right triangle, one angle is $90^\circ$ (at $\angle C$). 3. **Calculate $\angle B$ using the angle sum:** $$\angle A + \angle B + \angle C = 180^\circ$$ $$30^\circ + \angle B + 90^\circ = 180^\circ$$ 4. **Simplify to find $\angle B$:** $$\angle B = 180^\circ - 90^\circ - 30^\circ$$ $$\angle B = 60^\circ$$ 5. **Answer:** The measure of $\angle B$ is $60.0^\circ$ (rounded to one decimal place).