From construction
AB = XB (Since B is a point on the perpendicular bisector of AX)
⇒∠BAX=∠AXB (angles opposite to equal sides are equal)
∠ABC=∠BAX+∠AXB=2∠AXB=∠LXY
( ∵ XA is the bisector of the ∠LXY )
Therefore, ∠ABC=75∘
Similarly, ∠ACB=∠MYX
Therefore, ∠BCA=60∘
In △ ABC, we have,
∠ABC+∠BCA+∠CAB=180∘
75∘+60∘+∠CAB=180∘
Then ∠CAB=180∘−135∘
Therefore ∠CAB=45∘