In Fig. 7.48, sides AB and AC of Δ ABC are extended to points P and Q respectively. Also, ∠ PBC <∠ QCB. Show that AC > AB.

Question

In Fig. 7.48, sides AB and AC of &#x394; ABC are extended to points P and Q respectively. Also, &#x2220; PBC < &#x2220; QCB. Show that AC > AB.

Philoid · Accepted Answer

It is given in the question that:

∠PBC < ∠QCB

Now,

∠ABC + ∠PBC = 180^o

∠ABC = 180^o - ∠PBC

Also,

∠ACB + ∠QCB = 180^o

∠ACB = 180^o - ∠QCB

Since,

∠PBC < ∠QCB therefore,

∠ABC > ∠ACB

Thus,

AC > AB as sides opposite to the larger angle is larger