Adjacent Angles D0589F

1. **Stating the problem:** We need to determine the relationship between two adjacent angles when their exterior sides are perpendicular. 2. **Understanding the problem:** Adjacent angles share a common vertex and a common side. The exterior sides are the sides opposite the common side. 3. **Key fact:** If the exterior sides of adjacent angles are perpendicular, then the two exterior sides form a right angle, i.e., $$90^\circ$$. 4. **Formula and reasoning:** The sum of the two adjacent angles plus the angle between their exterior sides equals $$180^\circ$$ because they form a straight line. 5. Since the exterior sides are perpendicular, the angle between them is $$90^\circ$$. 6. Let the two adjacent angles be $$\alpha$$ and $$\beta$$. Then: $$\alpha + \beta + 90^\circ = 180^\circ$$ 7. Simplify: $$\alpha + \beta = 180^\circ - 90^\circ = 90^\circ$$ 8. **Conclusion:** The adjacent angles are complementary, meaning their sum is $$90^\circ$$. **Final answer:** The angles are complementary.