Question

If the side BC of ΔABC is produced on both sides, then write the difference between the sum of the exterior angles so formed and ∠A.

Answer 1

In the given problem, we need to find the difference between the sum of the exterior angles and∠A.

Now, according to the exterior angle theorem

 ext. ∠C = ∠A + ∠B              .........(1)

Also,

ext. ∠B = ∠A + ∠C               .........(2)

Further, adding (1) and (2)

 ext. ∠C + ext. ∠B = ∠A + ∠B + ∠A + ∠B       

 =2∠A+ ∠B + ∠C                  .........(3)

Also, according to the angle sum property of the triangle, we get,

∠A + ∠B + ∠C = 180°           .........(4)

Now, we need to find the difference between the sum of the exterior angles and ∠A 

Thus, 

( ext. ∠C + ext. ∠B) - ∠A = (2∠A + ∠B + ∠C ) - ∠A 

= ∠A = ∠B + ∠C       

   = 180°(Using 4)

Therefore,  (ext. ∠C ext.∠B) -∠A = 180°