Question

ray bd bisects ∠abc so that m∠dbc=(x + 6) and m∠abd=(2x - 12). what is x? a. 12 b. 14 c. 16 d. 18

Explanation:

Step1: Set up equation

Since ray $BD$ bisects $\angle ABC$, then $m\angle DBC=m\angle ABD$. So we set up the equation $x + 6=2x-12$.

Step2: Isolate $x$ terms

Subtract $x$ from both sides: $x+6 - x=2x - 12-x$, which simplifies to $6=x - 12$.

Step3: Solve for $x$

Add 12 to both sides: $6 + 12=x-12 + 12$, so $x = 18$.

Answer:

D. 18