Question

If the base of an isosceles triangle is produced on both sides, Prove that the exterior angles so formed are equal to each other.

Answer 1

$\begin{array}{c}In\Delta ABC\\ SideAB=AC\\ \angle B=\angle C=a\\ DBCisastraightline\\ x+a={180}^{\circ }\\ x=180-a\to \left(i\right)\\ Similarly\\ y+a={180}^{\circ }\\ y=180-a\to \left(ii\right)\\ fromequation\left(i\right)and\left(ii\right)\\ x=y=180-a\end{array}$