Question

bd bisects ∠abc. find m∠abd, m∠cbd, and m∠abc. m∠abc=(25x + 34)°. m∠abd=□°. m∠cbd=□°. m∠abc=□°

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{BD}$ bisects $\angle ABC$, then $m\angle ABD=m\angle CBD$ and $m\angle ABC = 2m\angle ABD=2m\angle CBD$. Also, $m\angle ABD=m\angle CBD = 11x + 23$ and $m\angle ABC=25x + 34$. So, $2(11x + 23)=25x + 34$.

Step2: Solve the equation for $x$

Expand the left - hand side: $22x+46 = 25x + 34$.
Subtract $22x$ from both sides: $46=3x + 34$.
Subtract 34 from both sides: $3x=46 - 34=12$.
Divide both sides by 3: $x = 4$.

Step3: Find $m\angle ABD$

Substitute $x = 4$ into the expression for $m\angle ABD$: $m\angle ABD=11x + 23=11\times4+23=44 + 23=67^{\circ}$.

Step4: Find $m\angle CBD$

Since $m\angle ABD=m\angle CBD$, then $m\angle CBD = 67^{\circ}$.

Step5: Find $m\angle ABC$

Substitute $x = 4$ into the expression for $m\angle ABC$: $m\angle ABC=25x + 34=25\times4+34=100 + 34=134^{\circ}$.

Answer:

$m\angle ABD = 67^{\circ}$
$m\angle CBD = 67^{\circ}$
$m\angle ABC = 134^{\circ}$