Question

Prove that when two lines intersect, the vertically opposite angles are equal.

Answer 1

We have to prove $\angle 1=\angle 3\&\angle 2=\angle 4$

$\angle 1+\angle 2={180}^{\circ }$ .......(i) [Linear pair]

$\Rightarrow \angle 1={180}^{\circ }-\angle 2$

Again, $\angle 3+\angle 2={180}^{\circ }$ .......(ii) [Linear pair]

$\Rightarrow \angle 3={180}^{\circ }-\angle 2$

Hence, $\angle 1=\angle 3$ [from (i) and (ii)]

Similarly, we can prove that $\angle 2=\angle 4$.