In the given construction of a ΔABC, ∠CAB will be
In ΔAXB
PQ is the perpendicular bisector of XA, the two triangles formed are congruent by SAS rule.
∴ AB = XB
⇒ ∠BAX=∠AXB
∠ABC=∠BAX+∠AXB
= 2 ∠AXB=∠LXY
[Since ∠AXB is angle bisector of ∠LXY]
Similarly, ∠ACB=∠MYXTherefore, ∠ABC=75∘ and ∠BCA=60∘In ΔABC, we have∠ABC+∠BCA+∠CAB=180∘75∘+60∘+∠CAB=180∘∠CAB=180∘−135∘∠CAB=45∘