Chapter SR20, Problem 3P

Solution

  $\overrightarrow{BD}$ is the angle bisector of $\angle ABC$ . Find the value of x.

  $x=8^o$

Given:

The given angle.

  

Concept Used:

• Angle bisector is a ray that divides an angle into two congruent angles.

Calculation:

The given angle is −

  

As $\angle ABD={(11x-19)}^0$

And $\angle DBC={(8x+5)}^0$

  $\overrightarrow{BD}$ is the angle bisector of $\angle ABC$ .

So $\angle ABD=\angle DBC$

  $\begin{array}{c}$ {(11x-19)}^0={(8x+5)}^0$11x-19=8x+5\\ 11x-8x=5+19\\ 3x=24\\ x=\frac{24}{3}\\ x=8\end{array}$

  $x=8^o$