in a rhombus abcd, ac=ad. find the measurment of angle b and angle dcb.

Answer : 

We have rhombus  ABCD , So 

AB =  BC  =  CD  = AD                      ------------ ( 1 )

And 

Given AC  =  AD                               ------------- ( 2 ) , So


In $∆$ ABC

AB  =  BC  =  AC , So ​$∆$ ABC is a equilateral triangle  and we know all internal angles of equilateral triangle are at 60$°$

So, $\angle$ BAC =  ​$\angle$ BCA = ​ ​$\angle$ABC  = 60​$°$

Similarly 
$∆$ ADC is a equilateral triangle ,  So 
$\angle$ DAC =  ​$\angle$DCA = ​ ​$\angle$ADC  = 60​$°$

So,
​ ​$\angle$DCB = $\angle$BCA + $\angle$DCA  = 60​$°$ + 60$°$ =  120$°$

And 

$\angle$B  = 60$°$