Question

m∠abc = 40° and bd is the angle bisector of ∠abc
x = ?

Explanation:

Step1: Recall angle - bisector property

An angle - bisector divides an angle into two equal angles. So, if $\overrightarrow{BD}$ is the angle - bisector of $\angle ABC$ and $m\angle ABC = 40^{\circ}$, then $m\angle ABD=m\angle DBC = 20^{\circ}$.
We assume that either $3x + 6=20$ or $3x-1 = 20$ or $3x - 2=20$ or $5x-18 = 20$.
Let's solve each equation one - by - one.

Equation 1: Solve $3x + 6=20$

Subtract 6 from both sides:
$3x=20 - 6$
$3x=14$
$x=\frac{14}{3}\approx4.67$

Equation 2: Solve $3x-1 = 20$

Add 1 to both sides:
$3x=20 + 1$
$3x=21$
$x = 7$

Equation 3: Solve $3x-2 = 20$

Add 2 to both sides:
$3x=20+2$
$3x=22$
$x=\frac{22}{3}\approx7.33$

Equation 4: Solve $5x-18 = 20$

Add 18 to both sides:
$5x=20 + 18$
$5x=38$
$x=\frac{38}{5}=7.6$
We assume that the correct equation based on the geometric relationship is $3x - 1=20$ (since we need to find the value of $x$ that makes one of the sub - angles equal to $20^{\circ}$).

Answer:

$x = 7$