Question

what is the answer for this question. ..write it in detail

Answer 1

here angleBCD=angleADC
 and  angleACB= angleBDA
THEN 
angleACD=angleBDC
and both triangles have same base
TRIANGLES WITH SAME BASE AND ONE ANGLE
WE KNOW THAT
SIDES OPPOSITE TO EQUAL ANGLES ARE EQUAL
AD IS OPPOSITE TO ANGLE ACD  
AND  BC IS OPPOSITE TO ANGLE  BDC
SO
AD=BC

Answer 2

angle BCD=angle ADC         -(1)
angle ACB=angle BDA          -(2)
adding 1 and 2
angle ACD=angle BDC or angle C=angle D

in triangle ACD & BDC
angle C=angle D
angle BCD = angle ADC         (given)
CD=CD                                     (common)
therefore,triangle ACD congruent to triangle BDC
by CPCT, AD = BC       proved