Question

in the given figure sides ab and ac of a triangle are extended to point p and Q respectively also angle pbc angle q cb show that AC angle ab ​

Answer 1

Step-by-step explanation:

∠PBC is the exterior angle of △ABC.

Since exterior angle is sum of interior opposite angles.

So,

∠PBC=∠A+∠ACB

similarly,

∠QCB is the exterior angle of △ABC

So,

∠QCB=∠A+∠ABC

Now,

⇒ ∠PBC<∠QCB

⇒ ∠A+∠ABC<∠A+∠ACB

⇒ ∠ABC<∠ACB

On writing the opposite sides of the angles, we get

⇒ AB<AC

Hence proved.