If I is in the incentre of ΔABC with ∠A = 46°, then ∠BIC = ?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 113°
| Application |
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According to question:
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In ΔABC ∠A = 46° So, ∠B + ∠C = 180 - 46 ⇒ ∠B + ∠C = 134° |
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In ΔIBC: ∠BIC + ∠IBC + ∠BCI = 180 Here ∠IBC + ∠BCI = 1/2(∠B + ∠C) |
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⇒ ∠BIC + 67 = 180 ⇒ ∠BIC = 180 - 67 ⇒ ∠BIC = 113° |
Direct formula:
∠BIC = 90 + ∠BAC/2 = 90 + 46/2 = 113°