Please find the attachment for the accompanying diagram of this question. From the diagram we can see that [tex] \angle EDF [/tex] and [tex] \angle ADC [/tex] are vertically opposite angles.
Thus, [tex] \angle EDF=\angle ADC[/tex]
Now, we know that the value of [tex] \angle EDF[/tex]=120 degrees (given)
We also know that [tex] \angle ADC[/tex] is the sum of two angles, [tex] \angle ADB[/tex] and [tex] \angle BDC [/tex], thus we have:
120=[tex] \angle ADB[/tex] + [tex] \angle BDC[/tex]
Now we are given that [tex] \angle ADB [/tex]=3x and [tex] \angle BDC [/tex]=2x, thus the above equation becomes
[tex] 120=3x+2x [/tex]
[tex] 5x=120 [/tex]
therefore x=24
Thus we have proved that x=24 degrees as required
