Question

$\overrightarrow{DB}$bisects $\angle ADC,m\angle 1=5x-3,\text{\hspace{0.33em}and}m\angle 2=x+25$. Find the value of $x$.

Short answer

The number 7 represents itself as the value of $x$.

Step-by-step solution

Step 1. Observe the given information.

The given information represents $\overrightarrow{DB}$as a bisector which means the angles bisects by the line$\overrightarrow{DB}$ are equal to each other.

Step 2. Make an equation by using the observation.

Equate the measurement of angles bisects by the line $\overrightarrow{DB}$equal to each other. The angles are $\angle 1$and $\angle 2$.

$m\angle 1=m\angle 2$

Step 3. Determine the number that represents the value of x by using the obtained equation.

Substitute the value of $m\angle 1$and localid="1649242247308" $m\angle 2$into the equation $m\angle 1=m\angle 2$ and determine the number that represents the value of $x$.

localid="1649242020481" $\begin{array}{c}5x-3=x+25\\ 5x-x=25+3\\ 4x=28\\ x=\frac{28}{4}\\ x=7\end{array}$