Question

bd bisects ∠abc. find m∠abd, m∠cbd, and m∠abc.

m∠abd =

m∠cbd =

m∠abc =

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{BD}$ bisects $\angle ABC$, we have $m\angle ABD=m\angle CBD$. So, $6x + 14=3x+29$.

Step2: Solve for $x$

Subtract $3x$ from both sides: $6x-3x + 14=3x-3x + 29$, which simplifies to $3x+14 = 29$. Then subtract 14 from both sides: $3x+14 - 14=29 - 14$, giving $3x=15$. Divide both sides by 3: $x = 5$.

Step3: Find $m\angle ABD$

Substitute $x = 5$ into the expression for $m\angle ABD$: $m\angle ABD=6x + 14=6\times5+14=30 + 14=44^{\circ}$.

Step4: Find $m\angle CBD$

Since $m\angle CBD=m\angle ABD$, $m\angle CBD = 44^{\circ}$.

Step5: Find $m\angle ABC$

$m\angle ABC=m\angle ABD + m\angle CBD=44^{\circ}+44^{\circ}=88^{\circ}$.

Answer:

$m\angle ABD = 44^{\circ}$
$m\angle CBD = 44^{\circ}$
$m\angle ABC = 88^{\circ}$