Question

look at this diagram: if jl and mo are parallel lines and m∠lkn = 112.4°, what is m∠mhk?

Explanation:

Step1: Identify angle - relationship

$\angle LKN$ and $\angle MNH$ are vertical angles. Vertical angles are equal. So, $m\angle MNH=m\angle LKN = 112^{\circ}$.

Step2: Use linear - pair property

$\angle MNH$ and $\angle MNI$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. Let $m\angle MNI=x$. Then $m\angle MNH + x=180^{\circ}$. Substituting $m\angle MNH = 112^{\circ}$, we get $112^{\circ}+x = 180^{\circ}$, so $x=180^{\circ}-112^{\circ}=68^{\circ}$.

Step3: Identify corresponding angles

$\angle MNI$ and $\angle MIK$ are corresponding angles. Since $\overleftrightarrow{JL}\parallel\overleftrightarrow{MO}$, corresponding angles are equal. So, $m\angle MIK=m\angle MNI = 68^{\circ}$.

Answer:

$68$