 Suggested languages for you:

Europe

Answers without the blur. Sign up and see all textbooks for free! Q9

Expert-verified Found in: Page 46 ### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279 # State the number that is paired with the bisector of $\angle CDE$. The number paired with the bisector of $\angle CDE$ is $60°$.

See the step by step solution

## Step 1. State the given information. $\angle CDF={80}^{\circ }$

$\angle EDF=40°$

## 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 $\angle CDE$ as shown in Figure-2 here, Assume $\angle BDF=z°$.

Let $\angle CDB=x°$

That implies

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

Then,

$\angle EDF+\angle BDE+\angle CDB=40°+x°+x°$

Again,

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

$=80°$

Then,

$40°+x°+x°=80°$

$40°+2x°=80°$

$2x°=40°$

$x°=20°$

## Step 3. State the conclusion.

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

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

$z°=40°+20°$

$=60°$

Therefore, the number paired with the bisector of $\angle CDE$ is $60°$ ### Want to see more solutions like these? 