Answer
(a) complement: $\frac{5\pi}{12}$
supplement: $\frac{11\pi}{12}$
(b) There is no complement of $\frac{11\pi}{12}$ because $\frac{11\pi}{12}\gt\frac{\pi}{2}$
supplement: $\frac{\pi}{12}$
Work Step by Step
(a) complement: $\frac{\pi}{2}-θ=\frac{\pi}{2}-\frac{\pi}{12}=\frac{6\pi}{(6)2}-\frac{\pi}{12}=\frac{6\pi}{12}-\frac{\pi}{12}=\frac{5\pi}{12}$
supplement: $\pi-θ=\pi-\frac{\pi}{12}=\frac{12\pi}{12}-\frac{\pi}{12}=\frac{11\pi}{12}$
(b) complement: There is no complement of $\frac{11\pi}{12}$ because $\frac{11\pi}{12}\gt\frac{\pi}{2}$
supplement: $\pi-θ=\pi-\frac{11\pi}{12}=\frac{12\pi}{12}-\frac{11\pi}{12}=\frac{\pi}{12}$
