# Chapter 6 - 6.1 - Angles and Their Measure - 6.1 Exercises - Page 431: 57

(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: $\pi-θ=\pi-\frac{11\pi}{12}=\frac{12\pi}{12}-\frac{11\pi}{12}=\frac{\pi}{12}$

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