Question

determine the measure of ∠abc if ∠dba = 5x + 3 and ∠dbc = 2x + 12. (hint: find x first)

Explanation:

Step1: Set up equation from angle - bisector property

Since $\angle DBA=\angle DBC$ (angle - bisector), we have $5x + 3=2x+12$.

Step2: Solve for $x$

Subtract $2x$ from both sides: $5x-2x + 3=2x-2x + 12$, which simplifies to $3x+3 = 12$. Then subtract 3 from both sides: $3x+3 - 3=12 - 3$, getting $3x=9$. Divide both sides by 3: $x=\frac{9}{3}=3$.

Step3: Find $\angle ABC$

$\angle ABC=\angle DBA+\angle DBC$. Substitute $x = 3$ into the expressions for $\angle DBA$ and $\angle DBC$. $\angle DBA=5x + 3=5\times3+3=15 + 3=18^{\circ}$, $\angle DBC=2x + 12=2\times3+12=6 + 12=18^{\circ}$. So $\angle ABC=18^{\circ}+18^{\circ}=36^{\circ}$.

Answer:

D. $\angle ABC = 36^{\circ}$