Question

bd bisects ∠abc. use x to find the measure of ∠abc. m∠abc = type your answer.

Explanation:

Step1: Set up equation based on angle - bisector property

Since $\overrightarrow{BD}$ bisects $\angle ABC$, then $\angle ABD=\angle DBC$. So, $7x - 4=4x + 11$.

Step2: Solve the equation for $x$

Subtract $4x$ from both sides: $7x-4x - 4=4x-4x + 11$, which simplifies to $3x-4 = 11$. Then add 4 to both sides: $3x-4 + 4=11 + 4$, giving $3x=15$. Divide both sides by 3: $x = 5$.

Step3: Find the measure of $\angle ABC$

$\angle ABC=\angle ABD+\angle DBC$. Since $\angle ABD=\angle DBC$, and $\angle ABD = 7x - 4$ and $\angle DBC=4x + 11$. Substitute $x = 5$ into either expression for $\angle ABD$ or $\angle DBC$. Let's use $\angle ABD$: $\angle ABD=7\times5-4=35 - 4=31^{\circ}$. Then $\angle ABC = 2\angle ABD=2\times31^{\circ}=62^{\circ}$.

Answer:

$62^{\circ}$