Question

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

Short answer

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

Step-by-step solution

Step 1. State the given information.

$\angle CDF=120°$

$\angle EDF=30°$

Step 2. State the assumptions and the calculations.

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

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

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

Assume $\angle BDF=z°$.

Let $\angle CDB=x°$

That implies

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

Then,

$\angle EDF+\angle BDE+\angle CDB=30°+x°+x°$

Again,

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

$=120°$

Then,

$30°+x°+x°=120°$

$30°+2x°=120°$

$2x°=90°$

$x°=45°$

Step 3. State the conclusion.

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

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

$z°=30°+45°$

$=75°$

Therefore, the number paired with the bisector of $\angle CDE$is $75°$