Question

Can anyone help me with this problem ?

Answer 1

Come now !  I'm sure you could unravel it if you look at it and think about it
for a minute or two.

What's an angle bisector ?  It's a line that splits an angle exactly in half.
The two little angles on each side of it are EQUAL.  Each of them is exactly
half of the big angle.

So in this drawing,    (3/2 x - 6)    is equal to    (1/4 x + 4) .
Do you think you could find 'x' ?

3/2 x - 6  =  1/4 x + 4

Add 6 to each side of the equation:    3/2 x = 1/4 x + 10

Multiply each side by 4 :                     6 x = x + 40

Subtract 'x' from each side:                  5 x = 40

Divide each side by 5 :                          x = 8

Angle  CBD  is  1/4 x + 4 .  That's  1/4 (8) + 4 = 2 + 4 = 6 degrees