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प्रश्न
In ΔABC, if bisectors of ∠ABC and ∠ACB intersect at O at angle of 120°, then find the measure of ∠A.
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उत्तर
In the given ΔABC, ∠ABC = ∠ACB, the bisectors of ∠ABC and ∠ACBmeet at O and ∠BOC = 120°
We need to find the measure of ∠A
So here, using the corollary, “if the bisectors of ∠ABCand ∠ACBof a ΔABCmeet at a point O, then`∠BOC = 90° + 1/2 ∠A`
Thus, in ΔABC
`∠BOC = 90° + 1/2 ∠A`
` 120° = 90° + 1/2 ∠A`
`120° - 90° + 1/2 ∠A`
∠A = 2(30°)
∠A= 60°
Thus, ∠A = 60°
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