Chapter 2.4, Problem 8CE

a.

To determine

To write:The name of supplement of $\angle MLQ$ from given figure.

Answer to Problem 8CE

The angle $\angle LQP$ is the supplementary angle of $\angle MLQ$ .

Explanation of Solution

Given:

The given figure is shown here.

Concept used:

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:

Calculations:

From the given figure,

  $\angle MLP={40}^0$

Given

  $\angle PLQ={60}^0$

Given

  $\angle MLP+\angle PLQ={40}^0+{60}^0$

  $\Rightarrow \angle MLP+\angle PLQ={100}^0$

  $\Rightarrow \angle MLQ={100}^0$ … (1)

Now, $\angle LQP={80}^0$

Given

  $\Rightarrow \angle MLQ+\angle LQP={100}^0+{80}^0$

  $\Rightarrow \angle MLQ+\angle LQP={180}^0$

Since, $\angle MLQ+\angle LQP={180}^0$ therefore $\angle MLQ$ and $\angle LQP$ are supplementary angles.

Thus, $\angle LQP$ is the supplementary angle of $\angle MLQ$ .

Conclusion:

The angle $\angle LQP$ is the supplementary angle of $\angle MLQ$ .