Question

1. s are congruent: find x = m∠cbd m∠abd

Explanation:

Step1: Set up equation based on angle - congruence

Since $\angle ABD$ and $\angle CBD$ are congruent, and $\angle ABD = 5x$ and $\angle CBD=x$, we know that $5x + x=180^{\circ}$ (because they are a linear - pair of angles and linear - pair of angles are supplementary).
$5x+x = 180$
$6x=180$

Step2: Solve for $x$

Divide both sides of the equation $6x = 180$ by 6.
$x=\frac{180}{6}=30$

Step3: Find $m\angle CBD$

Substitute $x = 30$ into the expression for $m\angle CBD$. Since $m\angle CBD=x$, then $m\angle CBD = 30^{\circ}$

Step4: Find $m\angle ABD$

Substitute $x = 30$ into the expression for $m\angle ABD$. Since $m\angle ABD = 5x$, then $m\angle ABD=5\times30 = 150^{\circ}$

Answer:

$x = 30$
$m\angle CBD=30^{\circ}$
$m\angle ABD = 150^{\circ}$