1. **Problem Statement:** We have a right triangle ABC with a right angle at C. Given: side AC = 18 units, angle A = 30°, 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°. Since angle C is 90°, we have: $$m\angle A + m\angle B + m\angle C = 180^\circ$$ 3. **Apply the rule:** Substitute the known values: $$30^\circ + m\angle B + 90^\circ = 180^\circ$$ 4. **Solve for $m\angle B$:** $$m\angle B = 180^\circ - 90^\circ - 30^\circ$$ $$m\angle B = 60^\circ$$ 5. **Answer:** The measure of angle B is $60.0^\circ$ (rounded to one decimal place).