Question

1. line segment bd bisects ∠abc. what is the value of x? x =

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{BD}$ bisects $\angle ABC$, then $\angle ABD=\angle DBC$. So, $9x + 24=15x-12$.

Step2: Solve the equation for $x$

First, move the $x$ - terms to one side and the constants to the other side. Subtract $9x$ from both sides: $24 = 15x-9x - 12$. Then simplify to get $24=6x - 12$. Add 12 to both sides: $24 + 12=6x$, which gives $36 = 6x$. Divide both sides by 6: $x=\frac{36}{6}$.

Answer:

$x = 6$