Question

look at this diagram: if ik and ln are parallel lines and m∠lmj = 126°, what is m∠nmj?

Explanation:

Step1: Recall linear - pair property

$\angle LMJ$ and $\angle NMJ$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$.
$m\angle LMJ + m\angle NMJ=180^{\circ}$

Step2: Solve for $\angle NMJ$

Given $m\angle LMJ = 126^{\circ}$, we substitute into the equation:
$m\angle NMJ=180^{\circ}-m\angle LMJ$
$m\angle NMJ = 180 - 126$
$m\angle NMJ = 54^{\circ}$

Answer:

$54$