Question

2) In the given figure, O is the centre of the circle. If EBC = 108
and AOB = 92°, calculate the value of BDC.
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Answer 1

Answer:

The answer will be BDC= 54°

Answer 2

Join BD.

∠ADC = ∠EBC = 108° (The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle)

∠ADB = $\frac{1}{2}$ × ∠AOB =$\frac{1}{2}$ ×92° = 46° ( Angles subtended by chord AB at centre and on the circumference)

∠BDC = ∠ADC - ∠ADB = 108° - 46° = 62°