Question : In $\triangle$ABC, $\angle$B = 35°, $\angle$C = 65° and the bisector of $\angle$BAC meets BC in D. Then $\angle$ADB is:
Option 1: 40°
Option 2: 75°
Option 3: 90°
Option 4: 105°
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Correct Answer: 105°
Solution :
Given:
In $\triangle$ABC, $\angle$B = 35°, $\angle$C = 65°
So, $\angle$A = 180° – 35° – 65° = 80°
The bisector of $\angle$BAC meets BC in D.
∴ $\angle$BAD = $\frac{1}{2}×\angle$A = $\frac{1}{2}$ × 80° = 40°
Therefore $\angle$ADB = 180° – $\angle$BAD – $\angle$B
⇒ $\angle$ADB = 180° – 40° – 35°
∴ $\angle$ADB = 105°
Hence, the correct answer is 105°.
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