Question

State the number that is paired with the bisector of $\angle CDE$.

Short answer

The number paired with bisector of $\angle CDE$ is $70°$.

Step-by-step solution

Step 1. Observe the diagram.

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

Step 2. State the assumptions and the calculations.

For the calculation, the concept used is the definition of the bisector angle.

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

From Figure-2:

$\angle CDF=122°$

$\angle EDF=18°$

Assume $\angle BDF=z°$.

Let $\angle CDB=x°$

That implies

$\angle BDE=x°$ [ since DB is the bisector of $\angle CDE$]

Then,

$\angle EDF+\angle BDE+\angle CDB=18°+x°+x°$

Again,

$\angle EDF+\angle BDE+\angle CDB=\angle CDF$

$=122°$

Then,

$18°+x°+x°=122°$

$18°+2x°=122°$

$2x°=104°$

$x°=52°$

Step 3. State the conclusion.

It is known that $\angle BDF=\angle BDE+\angle EDF$, then,

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

$z°=18°+52°$

$=70°$

Therefore, the number paired with the bisector of $\angle CDE$is$70°$