Question

in figure,AB divides angle DAC in the ratio of angle DAB : angle BAC = 1:3 and AB = DB .find the value of x​

Answer 1

Answer:

∠DAC=180°−108°=72°

∠BAC/∠DAB=1/3Given

∠DAB=3∠BAC

∴∠BAC+∠DAB=∠DAC=72°

⇒∠BAC+3∠BAC=72°

⇒4∠BAC=72°

⇒∠BAC=72/4=18°

∴∠DAB=3×18°=54

°∴∠DAB=∠BDA=54°(AB=DB)

∴∠ABD=180°−(54°+54°)

=180−108°=72°

 ∠DBA=72°=∠BAC+x (Exterio angle)

⇒x=72°−18°=54°

I hope I have solved your problem