91Ó°ÊÓ

The given diagram is:

The supplementary angles are the angles whose sum is 180°.

∠1 is supplementary to∠3.

Therefore, the sum of angles ∠1 and ∠3 is 180°.

That implies,

$∠1+∠3=180°\left(1\right)$

∠2 is supplementary to∠3.

Therefore, the sum of angles ∠2 and ∠3 is 180°.

That implies,

$∠2+∠3=180°\left(2\right)$

From the equations (1) and (2), it is obtained that:

$\begin{array}{c}∠1+∠3=∠2+∠3\\ ∠1=∠2\end{array}$

That implies $∠1â‰\dots ∠2$.

From the given diagram it can be noticed that angles ∠1 and ∠2 are the adjacent angles.

Therefore, angles ∠1 and ∠2 are the adjacent congruent angles.

Now by using the theorem of the converse of perpendicular lines it can be said that if the angles ∠1 and ∠2 are the adjacent congruent angles, then the lines j and k are perpendiculars.

That implies $jâŠ\yen k$.