Question
Answer: Option B
:
B
In ΔAXB
PQ is the perpendicular bisector ofXA, the two triangles formed are congruentby SASrule.
∴ 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∘InΔABC,wehave∠ABC+∠BCA+∠CAB=180∘75∘+60∘+∠CAB=180∘∠CAB=180∘−135∘∠CAB=45∘
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:
B
In ΔAXB
PQ is the perpendicular bisector ofXA, the two triangles formed are congruentby SASrule.
∴ 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∘InΔABC,wehave∠ABC+∠BCA+∠CAB=180∘75∘+60∘+∠CAB=180∘∠CAB=180∘−135∘∠CAB=45∘
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