In the given circle with centre O, the obtuse angle at the centre measures 104°. In the quadrilateral drawn inside the circle, what is the measure of the angle opposite to ∠O? 

Correct option is B

Given:

The angle at the center of the circle, ∠AOB, is $$104^\circ.$$​​

Concept Used:

In a cyclic quadrilateral ,

Sum of opposite angles =$$180\degree$$

Angle at the Centre is Twice the Angle at the Circumference .

Solution:

Draw AD and DC.

∠ADC = ​​​$$\frac{104\degree}2$$ = $$52\degree$$ 

​​∠ADC + ∠ABC = $$180\degree$$​

​$$52\degree + ∠ABC = 180°$$   

∠ABC = $$180\degree - 52\degree =128\degree$$