Question

given that bd bisects ∠abc and m∠abd = x + 15 and m∠dbc = 4x - 12, what is the m∠abc? multiple choice 4 points

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{BD}$ bisects $\angle ABC$, then $m\angle ABD=m\angle DBC$. So we set up the equation $x + 15=4x-12$.

Step2: Solve the equation for $x$

Subtract $x$ from both sides: $15 = 3x-12$. Then add 12 to both sides: $3x=27$, and $x = 9$.

Step3: Find $m\angle ABC$

Since $m\angle ABC=m\angle ABD + m\angle DBC$ and $m\angle ABD=m\angle DBC=x + 15$ (or $4x-12$), substituting $x = 9$ into $m\angle ABD=x + 15$, we get $m\angle ABD=9 + 15=24$. Then $m\angle ABC=2m\angle ABD=48$.

Answer:

$48$