ABC is a right triangle, BC is perpendicular to CA, D lies on BA,...

[fasibasar]

ABC is a right triangle
BC is perpendicular to CA
D lies on BA
m(ABC) = 2alpha
m(DCA) = 3alpha
|BC| = a units
|AD| = b units
|AD| = a - b units

find the value of alpha

my work: I extended |DA|

https://postimg.org/image/lbhqbhf17/

 

[Harry_the_cat]

ABC is a right triangle
BC is perpendicular to CA
D lies on BA
m(ABC) = 2alpha
m(DCA) = 3alpha
|BC| = a units
|AD| = b units
|AD| = a - b units

find the value of alpha

my work: I extended |DA|

https://postimg.org/image/lbhqbhf17/

You say:
|AD| = b units
|AD| = a - b units

Which one is it?

 

[fasibasar]

You say:
|AD| = b units
|AD| = a - b units

Which one is it?

|AD| = a - b units
|AC|= b units

 

[fasibasar]

Make triangleABC a 30-60-90 triangle; assign AC = 1.

Can you calculate alpha ?

Alpha is 15 deg.But you can't make a triangle 30-60-90.It is not given.