Question

angle bisector and inverse hw
$overrightarrow{bx}$ bisects $angle abc$
if $angle abc = 4x - 12$ and $angle abx = 24$
$x=square$
$angle abc=square$

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{BX}$ bisects $\angle ABC$, then $\angle ABC = 2\angle ABX$.

Step2: Set up the equation

Given $\angle ABC=4x - 12$ and $\angle ABX = 24$, we have $4x-12=2\times24$.

Step3: Solve the equation for $x$

First, simplify the right - hand side: $4x-12 = 48$. Then add 12 to both sides: $4x=48 + 12$, so $4x=60$. Divide both sides by 4: $x=\frac{60}{4}=15$.

Step4: Find $\angle ABC$

Substitute $x = 15$ into the expression for $\angle ABC$: $\angle ABC=4x-12=4\times15-12=60 - 12=48$.

Answer:

$x = 15$
$\angle ABC=48$