Answer
m$\angle$DAC=115$^{\circ}$
Work Step by Step
m$\angle$BCD=m$\angle$DAC
m$\angle$A=m$\angle$C
m$\angle$B+m$\angle$A+m$\angle$C=180
50+2m$\angle$C=180
2m$\angle$C=130
m$\angle$C=65
m$\angle$BCD+m$\angle$DCA=m$\angle$C
m$\angle$BCD+m$\angle$DCA=65
m$\angle$DAC+m$\angle$DCA=65
m$\angle$DAC+m$\angle$DCA+m$\angle$ADC=180
65+m$\angle$ADC=180
m$\angle$DAC=115
