Question

look at this diagram: if $overleftrightarrow{ik}$ and $overleftrightarrow{ln}$ are parallel lines and $mangle{nmo}=110^{circ}$, what is $mangle{lmj}$?

Explanation:

Step1: Identify vertical - angle relationship

$\angle NMO$ and $\angle LMH$ are vertical angles. Vertical angles are equal. So $m\angle LMH=m\angle NMO = 110^{\circ}$.

Step2: Identify linear - pair relationship

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

Step3: Solve for $m\angle LMJ$

$m\angle LMJ=180^{\circ}-m\angle LMH$. Substitute $m\angle LMH = 110^{\circ}$ into the equation. Then $m\angle LMJ=180 - 110=70^{\circ}$.

Answer:

$70$