Question : In a triangle$\frac{AB}{AC}=\frac{BD}{DC}$, $\angle$B = 70° and $\angle$C = 50°, then $\angle$BAD =?
Option 1: 60°
Option 2: 20°
Option 3: 30°
Option 4: 50°
Correct Answer: 30°
Solution :
Given:
$\frac{AB}{AC}=\frac{BD}{DC}$
$\angle$A = 180° – $\angle$B – $\angle$C = 180° – 70° – 50° = 60°
We know that if a line through one of the vertex of a triangle divides the opposite side in the ratio of the other two sides, the line bisects the angle at the vertex.
$\therefore \angle$BAD = $\frac{1}{2} \angle$A = $\frac{1}{2}×60°=30°$
Hence, the correct answer is 30°.
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