Chapter 4.1, Problem 88E

To determine

To find the complement and supplement of the angle $\frac{\text{3π}}{\text{4}}\text{radian}$

Answer to Problem 88E

  ${45}^0$

Explanation of Solution

Given: The angle $\frac{\text{3π}}{\text{4}}\text{radian}$

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 $\frac{\text{3π}}{\text{4}}\text{radian}$ from radian to degree.

  $\begin{array}{l}\text{π}\text{radian}=180\mathrm{deg}\\ 1\text{radian}=\frac{180}{\text{π}}\mathrm{deg}\\ \frac{\text{3π}}{\text{4}}\text{radian}=\frac{\text{3π}}{\text{4}}·\frac{180}{\text{π}}\mathrm{deg}=135\mathrm{deg}\end{array}$

Here we cannot find the complement as the angle is more than 90 degrees. The sum of two complementary angles is 90 degrees.

Only we can find the supplement of the angle ${135}^0$

Supplement of angle ${135}^0$ = ${180}^0-{135}^0={45}^0$

Thus, the supplement of angle $\frac{\text{3π}}{\text{4}}\text{radian}$ or ${135}^0$ is ${45}^0$