Question

Side BC of a $\Delta ABC$ is produced in both the directions. Prove that the sum of the two exterior angles so formed is greater than ${180}^o$.

Answer 1

If we extend $BC$ on both ends, then the angles would be,

$\angle ACD=180-C$

$\angle ABF=180-B$

Sum of the $2$ exterior angles$=\angle ACD+\angle ABF$

$=(180-C)+(180-B)$

$=360-(B+C)$

$=360-(180-A)=180+A$

$\angle A$ is always positive.

$\therefore$ sum of the angles is greater than $180°$.