Question

⑥
m∠abd = 4x - 3
m∠dbc = 7x - 4
x =
m∠abd =

Explanation:

Step1: Note angle - relationship

$\angle ABD$ and $\angle DBC$ are a linear - pair, so $m\angle ABD + m\angle DBC=180^{\circ}$.
$(4x - 3)+(7x - 4)=180$

Step2: Combine like - terms

$4x+7x-3 - 4 = 180$
$11x-7 = 180$

Step3: Isolate the variable term

$11x=180 + 7$
$11x=187$

Step4: Solve for x

$x=\frac{187}{11}=17$

Step5: Find $m\angle ABD$

Substitute $x = 17$ into the expression for $m\angle ABD$.
$m\angle ABD=4x-3=4\times17-3=68 - 3=65$

Answer:

$x = 17$
$m\angle ABD=65$