Chapter 2.3, Problem 9WE

To determine

Towrite:The number that is paired with the bisector of given angle.

Answer to Problem 9WE

The number is paired with the bisector of $\angle CDE$ is 60.

Explanation of Solution

Given information:

The required number is paired with the bisector of $\angle CDE$ shown in Figure-1 here.

Conceptused:

Definition of bisector of an angle.

Calculations:

Suppose z is the number paired with the bisector of $\angle CDE$ as shown in Figure-2 here.

1   $\angle CDF={80}^0$  Given

2   $\angle EDF={40}^0$   Given

3   $\angle BDF=z^0$  Assumed

Suppose $\angle CDB=x^0$

4   $\Rightarrow \angle BDE=x^0$$\because$ DB is bisector of $\angle CDE$

5   $\angle EDF+\angle BDE+\angle CDB={40}^0+x^0+x^0$

6   $\angle EDF+\angle BDE+\angle CDB=\angle CDF={80}^0$

7   $\Rightarrow {40}^0+x^0+x^0={80}^0$

8   $\Rightarrow {40}^0+2x^0={80}^0$

9   $\Rightarrow 2x^0={80}^0-{40}^0$

10   $\Rightarrow 2x^0={40}^0$

11   $\Rightarrow \frac{2x^0}{2}=\frac{{40}^0}{2}$

12   $\Rightarrow x^0={20}^0$

Now,

$\angle BDF=\angle BDE+\angle EDF$

$\Rightarrow \angle BDF={40}^0+{20}^0={60}^0$

$\Rightarrow z=60$ .

Thus, the number is paired with the bisector of $\angle CDE$ is 60.

Conclusion:

The number is paired with the bisector of $\angle CDE$ is 60.