In ∆ABC, ∠B = 60°, ∠C = 40°, AL ⊥ BC and AD bisects ∠A such that L and D lie on side BC. Find ∠LAD.

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Solution

$We know that the sum of all angles of a triangle is 180 ° . Therefore, for △ ABC, we can say that : ∠ A + ∠ B + ∠ C = 180 ° Or, ∠ A + 60 ° + 40 ° = 180 ° \Rightarrow ∠ A = 80 ° ∠ DAC = \frac{∠ A}{2} (∵ AD bisects ∠ A) \Rightarrow ∠ DAC = \frac{80 °}{2} = 40 ° If we use the above logic on △ ADC, we can say that : ∠ ADC + ∠ DCA + ∠ DAC = 180 ° . (Sum of all the angles of △ ADC) ∠ ADC + 40 ° + 40 ° = 180 ° ∠ ADC = 180 ° - 80 ° = 100 ° ∠ ADC = ∠ ALD + ∠ LAD (Exterior angle is equal to the sum of two Interior opposite angles .) 100 ° = 90 ° + ∠ LAD (∵ AL ⊥ BC) ∠ LAD = 10 °$

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