HOW DO YOU SOLVE THIS PROBLEM find the value of x​

AC bisects ∠BAD, => ∠BAC=∠CAD (1)

thus in ΔABC and ΔADC,    ∠ABC=∠ADC (given),

                                      ∠BAC=∠CAD      [from (1)],

AC (opposite side side of ∠ABC) = AC (opposite side side of ∠ADC), the common side between ΔABC and ΔADC

Hence,      by AAS axiom, ΔABC ≅ ΔADC,

Therefore,  BC (opposite side side of ∠BAC) = DC (opposite side side of ∠CAD),  since (1)

Hence, BC=DC proved.