Question : In a triangle $ABC$, side $BC$ is produced to $D$ such that $\angle A C D=127^{\circ}$. If $\angle A B C=35^{\circ}$, then find $\angle B A C$.
Option 1: 82°
Option 2: 92°
Option 3: 95°
Option 4: 75°
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Correct Answer: 92°
Solution :
Given, In a triangle $ABC$, $\angle A C D=127^{\circ}$ and $\angle A B C=35^{\circ}$
By exterior angle property,
$\angle A C D = \angle A B C+\angle B A C$
$⇒127^{\circ} = 35^{\circ}+\angle B A C$
$⇒\angle B A C=127^{\circ} - 35^{\circ}$
$\therefore\angle B A C=92^{\circ}$
Hence, the correct answer is 92º.
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