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Question -

In ∆ABC, if bisectors of ∠ABC and ∠ACB intersect at O at angle of 120°, then find the measure of ∠A.



Answer -

In ∆ABC, bisectors of ∠B and ∠C intersect at O and ∠BOC = 120°
 
But ∠BOC = 90°+  
90°+  ∠A= 120°
⇒   ∠A= 120°-90° = 30°
∴ ∠A = 2 x 30° = 60°

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