Chapter 2.4, Problem 7CE

To determine

Towrite:The name of two complementary angles from given figure that are not adjacent.

Answer to Problem 7CE

The angles $\angle MLP$ , $\angle MPL$ are two complementary angles that are not adjacent.

Explanation of Solution

Given information:

The given figure is

Conceptused:

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

Calculations:

From the given figure, in $△LPM$

  $\angle MLP={40}^0$

Given

  $\angle MPL={50}^0$

Given

  $\angle MLP+\angle MPL+\angle LMP={180}^0$

Sum of angles of $△LPM$

  $={180}^0$

  ${40}^0+{50}^0+\angle LMP={180}^0$

  $\Rightarrow {90}^0+\angle LMP={180}^0$

  $\Rightarrow \angle LMP={180}^0-{90}^0$

  $\Rightarrow \angle LMP={90}^0$ … (1)

Since, $\angle MLP+\angle MPL={90}^0$ therefore $\angle MLP$ , $\angle MPL$ are complementary.

Also, $\angle MLP$ , $\angle MPL$ are not adjacent angles.

Thus, $\angle MLP$ , $\angle MPL$ are two complementary angles that are not adjacent.

Conclusion:

Theangles $\angle MLP$ , $\angle MPL$ are two complementary angles that are not adjacent.