We know that the segment DP is an angle bisector of angle BDC; this means that angle 1 has to be half angle BDC, that is:
[tex]m\angle1=\frac{1}{2}m\angle BDC[/tex]
Plugging the expresions given for each angle we have:
[tex]\begin{gathered} 6x+6=\frac{1}{2}(15x) \\ 12x+12=15x \\ 15x-12x=12 \\ 3x=12 \\ x=\frac{12}{3} \\ x=4 \end{gathered}[/tex]
Therefore, the value of x is 4
