Question

Prove that sum of all interior angles of a triangle equals to ${180}^{\circ }$

Answer 1

$\Delta CDE$ is a triangle.
Draw a line AB parallel to DE
Now, $\angle 1=\angle 4$ (Alternate Int. \angle s)
$\angle 2=\angle 5$ (Alternate Int. $\angle s$)
Now, $\angle 5+\angle 3+\angle 4={180}^{\circ }$
(linear pair)
$\Rightarrow \angle 2+\angle 3+\angle 1={180}^{\circ }$
$\Rightarrow$ sum of angles of a $\Delta$ is ${180}^{\circ }$