ABCD is a cyclic trapezium whose sides AD and BC are parallel to each other, if $$\angle ABC = 75^\circ$$ , then the measure of $$\angle BCD$$ is:

Given : $$\angle ABC = 75^\circ$$ and AD$$\parallel$$BC

To find : $$\angle$$ BCD = ?

Solution : In a cyclic quadrilateral, sum of opposite angles is supplementary.

=> $$\angle$$ ABC + $$\angle$$ ADC = $$180^\circ$$

=> $$\angle$$ ADC = $$180^\circ-75^\circ=105^\circ$$

Also, $$\angle$$ ADC + $$\angle$$ BCD = $$180^\circ$$     [Angles on the same side of transversal]

=> $$\angle$$ BCD =  $$180^\circ-105^\circ=75^\circ$$

=> Ans - (C)