Question : In a cyclic quadrilateral ABCD, the side AB is extended to a point X. If $\angle XBC=82°$ and $\angle ADB=47°$, then the value of $\angle BDC$ is:
Option 1: 40°
Option 2: 35°
Option 3: 30°
Option 4: 25°
Correct Answer: 35°
Solution :
Given: In a cyclic quadrilateral ABCD, $\angle XBC=82°$ and $\angle ADB=47°$.
A cyclic quadrilateral's exterior angle is equal to its opposite interior angle.
So, $\angle XBC= \angle ADC=82°$.
Also, $\angle ADB=47°$
⇒ $\angle BDC=82°-47°$
⇒ $\angle BDC=35°$
Hence, the correct answer is 35°.
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