Question

bd bisects ∠abc. use x to find the measure of ∠cbd. m∠cbd = type your answer...

Explanation:

Step1: Set up equation based on angle - bisector property

Since $\overrightarrow{BD}$ bisects $\angle ABC$, then $m\angle ABD=m\angle CBD$. So we set up the equation $7x - 4=4x + 11$.
$7x-4x=11 + 4$

Step2: Solve for $x$

Combining like - terms, we have $3x=15$. Dividing both sides by 3 gives $x = 5$.
$x=\frac{15}{3}=5$

Step3: Find the measure of $\angle CBD$

Substitute $x = 5$ into the expression for $m\angle CBD$ which is $4x+11$.
$m\angle CBD=4\times5 + 11=20 + 11=31^{\circ}$

Answer:

$31^{\circ}$