Q. 85.0( 2 Votes )

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

Answer :

Given that,

BC produced on both sides


We know that,


A + ABC + ACB = 180o (i)


ABD = A + ACB (Exterior angle theorem) (ii)


ACE = A + ABC (Exterior angle theorem) (iii)


Adding (ii) and (iii), we get


ABD + ACE = A + (A + ACB + ACB)


ABD + ACE = A + 180o


(ABD + ACE) - A = 180o


Thus, between the sum of the exterior angles so formed and A is 180o.


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