Question

In the given figure, if line $l\parallel$ line $m$, Show that $\angle 1+\angle 2-\angle 3={180}^o$.

Answer 1

Draw a parallel line to m passing through angle 2 such that it divides the angle into two parts in which one part is alternate interior angle of $\angle 3$ so it will be equal to $\angle 3$ and the remaining part would be equal to $\angle 2-\angle 3$

Also adjacent angle of $\angle 2-\angle 3$ will be alternate interior angle of $\angle 1$

and thus we can see that $\angle 1+\angle 2-\angle 3={180}^o$