Question : 
In the given figure, $\angle ABC=81^{\circ}$ and $\angle ACB=9^{\circ}$. What is the value of $\angle BDC$?
Option 1: 80°
Option 2: 90°
Option 3: 70°
Option 4: 60°
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Correct Answer: 90°
Solution :
The angles at the circumference subtended by the same arc are equal.
In $\triangle ABC$,
$\angle ABC + \angle BCA + \angle ACB = 180°$
⇒ $81° + 9° +\angle BAC= 180°$
⇒ $\angle BAC = 90°$
Now, $\angle BAC = \angle BDC = 90°$ (Angle made by the same arc on the same side of the circle are equal)
Hence, the correct answer is 90°.
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