We are given m<ABC is bisected by segment BD.
There form two angles m<ABD and m<CBD.
m<ABD = x-5.
m<CBD = 2x-6.
Angle bisector divide an angle into two equal angles.
Therefore,
Angle m<ABD = angle m<CBD
Plugging given values of m<ABD and m<CBD, we get
x-5 = 2x-6
Adding 6 on both sides, we get
x-5+6 = 2x-6+6
x+1 =2x.
Subtracting x from both sides, we get
x-x+1 =2x-x
1=x.
Therefore, the value of x is 1.
