Chapter 2.4, Problem 1CE

To determine

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

Answer to Problem 1CE

The measure of complement angle and supplement angle of angle $m\angle A=10$ are 80 and 170 respectively.

Explanation of Solution

Given information:

The measure of given angle $\angle A$ is $m\angle A=10$

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 $m\angle A=10$ .

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

  $m\left\{\text{comp}\angle A\right\}=\left(90-10\right)=80$

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

  $m\left\{\sup \angle A\right\}=\left(180-10\right)=170$

Conclusion:

The measure of complement angle and supplement angle of angle $m\angle A=10$ are 80 and 170 respectively.