11
Question
In the given construction of a ΔABC, ∠CAB will be
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Solution
The correct option is B
From construction
∠BAX=∠AXB(In ΔAXB,AB=XB, since PQ⊥XA)∠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∘
From construction
∠BAX=∠AXB(In ΔAXB,AB=XB, since PQ⊥XA)∠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∘
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