Chapter 2.3, Problem 10WE

To determine

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

Answer to Problem 10WE

The number is paired with the bisector of $\angle CDE$ is 75.

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.

  $\angle CDF={120}^0$  Given

  $\angle EDF={30}^0$  Given

  $\angle BDF=z^0$  Assumed

Suppose $\angle CDB=x^0$

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

Now, $\angle EDF+\angle BDE+\angle CDB={30}^0+x^0+x^0$

  $\Rightarrow \angle EDF+\angle BDE+\angle CDB=\angle CDF={120}^0$

  $\Rightarrow {30}^0+x^0+x^0={120}^0$

  $\Rightarrow {30}^0+2x^0={120}^0$

  $\Rightarrow 2x^0={120}^0-{30}^0$

  $\Rightarrow 2x^0={90}^0$

  $\Rightarrow \frac{2x^0}{2}=\frac{{90}^0}{2}$

  $\Rightarrow x^0={45}^0$

Now,

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

$\Rightarrow \angle BDF={30}^0+{45}^0={75}^0$

$\Rightarrow z=75$ .

Thus, the number is paired with the bisector of $\angle CDE$ is 75.

Conclusion:

The number is paired with the bisector of $\angle CDE$ is 75.