Question

# In ΔABC,AB=AC,∠A=40∘,O is a point inside ΔABC such that ∠OBC=∠OCA. Find the measure of ∠BOC.

A
110
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B
35
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C
140
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D
155
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Solution

## The correct option is A 110∘Given: AB = AC ∴∠ABC=∠ACB ...(i) {Angle opposite equal sides} Also, ∠OBC=∠OCA ...(ii) {given} Subtract (i) from (ii) ∠OBA=∠OCB ...(iii) Let ∠OBC=∠OCA=x and ∠OBA=∠OCB=y ∠ABC=∠ACB=x+y In △ABC, ∠ABC+∠BAC+∠BCA=180∘ {Using Angle Sum Property} 40∘ + (x + y) + (x + y) =180∘ ⇒2(x+y)=140∘ ⇒x+y=70∘ In △OBC, ∠OBC+∠OCB+∠BOC=180∘ ⇒x+y+∠BOC=180∘ ⇒∠BOC=180∘−(x+y) ⇒∠BOC=180∘−70∘=110∘

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