Suggested languages for you:

Americas

Europe

Q9

Expert-verifiedFound in: Page 46

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 $60\xb0$.

$\angle CDF={80}^{\circ}$

$\angle EDF=40\xb0$

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 $\angle BDF=z\xb0$.

Let $\angle CDB=x\xb0$

That implies

$\angle BDE=x\xb0$ [ since *DB* is bisector of $\angle CDE$ ]

Then,

$\angle EDF+\angle BDE+\angle CDB=40\xb0+x\xb0+x\xb0$

Again,

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

$=80\xb0$

Then,

$40\xb0+x\xb0+x\xb0=80\xb0$

$40\xb0+2x\xb0=80\xb0$

$2x\xb0=40\xb0$

$x\xb0=20\xb0$

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

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

$z\xb0=40\xb0+20\xb0$

$=60\xb0$

Therefore, the number paired with the bisector of $\angle CDE$ is $60\xb0$

94% of StudySmarter users get better grades.

Sign up for free