1. **State the problem:** We need to find the value of angle $c$ in a triangle where one interior angle is $24^\circ$ and the exterior angle adjacent to $c$ is $60^\circ$. 2. **Recall the exterior angle theorem:** The exterior angle of a triangle is equal to the sum of the two opposite interior angles. Here, the exterior angle $60^\circ$ equals the sum of $24^\circ$ and $c$. 3. **Set up the equation:** $$60 = 24 + c$$ 4. **Solve for $c$:** $$c = 60 - 24$$ $$c = 36$$ 5. **Conclusion:** The value of angle $c$ is $36^\circ$.