In the figure, sides AB and AC of △ ABC are extended to points P and Q respectively. Also, ∠ PBC < ∠ QCB. Show that AC > AB.

∠PBC < ∠QCB (Given)
Multiply the equation by -1.
⇒ - ∠PBC > - ∠QCB
Adding 180∘ on both sides, we get
∴ 180∘ - ∠PBC > 180∘ - ∠QCB
Angles on a straight line add to 180o
Sum of angles ∠PBC and ∠ABC is 180o.
Sum of angles ∠QCB and ∠ACB is 180o.
So, ⇒ ∠ABC > ∠ACB
⇒ AC > AB (Side opposite to greater angle is greater)
Hence Proved