Question

bd bisects ∠abc. solve for x and find m∠abc. m∠abc = (4x - 12)°, m∠abd = 24° x = \boxed{}

Explanation:

Step1: Define angle bisector relation

Since $\overrightarrow{BD}$ bisects $\angle ABC$, $m\angle ABC = 2 \times m\angle ABD$

Step2: Substitute given values

$4x - 12 = 2 \times 24$

Step3: Simplify right-hand side

$4x - 12 = 48$

Step4: Isolate term with x

$4x = 48 + 12$
$4x = 60$

Step5: Solve for x

$x = \frac{60}{4}$

Step6: Calculate $\angle ABC$

$m\angle ABC = 2 \times 24^\circ = 48^\circ$

Answer:

$x = 15$
$m\angle ABC = 48^\circ$