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प्रश्न
In the following figure, ΔABC is a triangle such that `(AB)/(AC) = (BD)/(DC)`, ∠B = 70°, ∠C = 50°. Find ∠BAD.
बेरीज
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उत्तर
We have, if a line through one vertex of a triangle divides the opposite side in the ratio of the other two sides, then the line bisects the angle at the vertex.
∴ ∠1 = ∠2
In ΔABC
∠A + ∠B + ∠C = 180°
⇒ ∠A + 70 ° + 50° = 180° [∵ ∠B = 70° and ∠C = 50°]
⇒ ∠A = 180° − 120° = 60°
⇒ ∠1 + ∠2 = 60°
⇒ ∠1 + ∠1 = 60° [∵ ∠1 = ∠2]
⇒ 2∠1 = 60°
⇒ ∠1 = 30°
∴ ∠BAD = 30°
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