1. **Problem Statement:** We need to find the measure of the exterior angle $q$ at the top vertex of the triangle. 2. **Key Concept:** The exterior angle of a triangle is equal to the sum of the two opposite interior angles. 3. **Given Angles:** The two opposite interior angles to $q$ are $63^\circ$ and $24^\circ$. 4. **Formula:** $$q = 63^\circ + 24^\circ$$ 5. **Calculation:** $$q = 87^\circ$$ 6. **Conclusion:** The measure of angle $q$ is $87^\circ$.