1. We are given that angle A measures 135° in the figure and we want to find the measure of angle B. 2. Assuming angles A and B are related and the problem suggests understanding their relationship, the most common scenario is that angles A and B are supplementary angles, meaning their measures add up to 180°. 3. Using the supplementary angle property: $$\text{Angle A} + \text{Angle B} = 180^\circ$$ 4. Substitute the known value of angle A: $$135^\circ + \text{Angle B} = 180^\circ$$ 5. Solve for angle B: $$\text{Angle B} = 180^\circ - 135^\circ = 45^\circ$$ 6. Therefore, angle B measures 45°.