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°

Question

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°

Team Careers360 · Accepted Answer

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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Question : In a cyclic quadrilateral ABCD, the side AB is extended to a point X. If ∠XBC=82° and ∠ADB=47°, then the value of ∠BDC is:Option 1: 40°Option 2: 35°Option 3: 30°Option 4: 25°

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Question : In a cyclic quadrilateral ABCD, the side AB is extended to a point X. If $∠ X B C = 82 °$ and $∠ A D B = 47 °$ , then the value of $∠ B D C$ is:
Option 1: 40°
Option 2: 35°
Option 3: 30°
Option 4: 25°