Question

1. bd bisects ∠abc. solve for m∠abc. (4x)° (3x + 11)°

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{BD}$ bisects $\angle ABC$, we have $\angle ABD=\angle DBC$. So, $4x = 3x + 11$.

Step2: Solve for $x$

Subtract $3x$ from both sides of the equation $4x=3x + 11$. We get $4x-3x=3x + 11-3x$, which simplifies to $x = 11$.

Step3: Find $\angle ABC$

Since $\angle ABC=\angle ABD+\angle DBC$ and $\angle ABD=\angle DBC$, and $\angle ABD = 4x$ and $\angle DBC=3x + 11$. Substitute $x = 11$ into either $\angle ABD$ or $\angle DBC$ and then double it. Using $\angle ABD = 4x$, when $x = 11$, $\angle ABD=4\times11 = 44^{\circ}$. So, $\angle ABC=2\times44^{\circ}=88^{\circ}$.

Answer:

$88^{\circ}$