UPSC 2013 CDS 2 Math Paper

In ΔABC
BC = BA(Given)
⇒ ∠BAC =∠BCA......(1)
Remember:
Equal sides have equal anglesopposite to them.
In ΔADC,
CD > AD (Given)
Remember:In a triangle, greater side has greater angle opposite to it.
⇒ ∠CAD > ∠ACD ......(2)
Adding (1) and (2), we have ∠BAC+∠CAD>∠BCA+∠ACD
⇒ ∠BAD > ∠BCD