Chapter 2.4, Problem 2WE

To determine

Tofind:The measures of a complement and a supplement angles of given angle $\angle K$ .

Answer to Problem 2WE

The measure of complement angle and supplement angle of angle $\angle K$ are $17\frac{1}{2}$ and $107\frac{1}{2}$ respectively.

Explanation of Solution

Given information:

The measure of given angle $\angle K$ is $m\angle K=72\frac{1}{2}=72.5$ .

Conceptused:

Complementary angles are two angles that have a sum of 90°. The measure complementary angle of $\angle X$ is $m\left\{\text{comp }\angle X\right\}=\left(90-X\right)$ . Supplementary angles are two angles that have a sum of 180°. The measure of a supplementary angle of $\angle Z$ is $m\left\{\sup \angle Z\right\}=180-Z$ .

Calculations:

The measure of given angle is $m\angle K=72\frac{1}{2}=72.5$ .

Therefore, the measure of complement angle of $\angle K$ is

  $m\left\{\text{comp}\angle K\right\}=\left(90-72.5\right)$

  $\Rightarrow m\left\{\text{comp}\angle K\right\}=17.5=17\frac{1}{2}$

The measure of supplement angle of $\angle K$ is

  $\begin{array}{l}m\left\{\sup \angle K\right\}=\left(180-72.5\right)\\ m\left\{\sup \angle K\right\}=107.5=107\frac{1}{2}\end{array}$

Conclusion:

The measure of complement angle and supplement angle of angle $\angle K$ are $17\frac{1}{2}$ and $107\frac{1}{2}$ respectively.