Chapter 4.1, Problem 90E

To determine

To find the complement and supplement of the angle $\frac{\text{π}}{\text{6}}\text{radian}$

Answer to Problem 90E

  ${60}^0$ ; ${150}^0$

Explanation of Solution

Given: The angle $\frac{\text{π}}{\text{6}}\text{radian}$

Concept Used:

Supplementary angles are two angles whose sum is 180 degrees while complementary angles are two angles whose sum is 90 degrees. 

Supplementary and complementary angles do not have to be adjacent (sharing a vertex and side, or next to), but they can be angles sum right angle.

Calculation:

Complementary angles are two angles that add to 90 degrees. Supplementary are two angles that add to 180 degrees.

Convert the angle $\frac{\text{π}}{\text{6}}\text{radian}$ from radian to degree.

  $\begin{array}{l}\text{π}\text{radian}=180\mathrm{deg}\\ 1\text{radian}=\frac{180}{\text{π}}\mathrm{deg}\\ \frac{\text{π}}{\text{6}}\text{radian}=\frac{\text{π}}{\text{6}}·\frac{180}{\text{π}}\mathrm{deg}=30\mathrm{deg}\end{array}$

Complement of angle ${30}^0$ = ${90}^0-{30}^0={60}^0$

Supplement of angle ${30}^0$ = ${180}^0-{30}^0={150}^0$

Thus, the complement and supplement of angle $\frac{\text{π}}{\text{6}}\text{radian}$ or ${30}^0$ are ${60}^0$ and ${150}^0$