line jl and line km intersect at point h. find the three unknown angle measures in the figure.\nfirst, find…

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. $\angle KHL$ and the $129^{\circ}$ angle are vertical angles. So $m\angle KHL = 129^{\circ}$.

Step2: Use the property of vertical angles

$\angle LHM$ and the $51^{\circ}$ angle are vertical angles. So $m\angle LHM=51^{\circ}$.

Step3: Use the property of a straight - line angle (sum of angles on a straight line is $180^{\circ}$)

For $\angle MHJ$, since $\angle MHJ$ and $\angle KHL$ form a straight line. Let $m\angle MHJ = x$. Then $x + 51^{\circ}=180^{\circ}$ (because $\angle KHL = 129^{\circ}$ and $\angle MHJ$ and $\angle KHL$ are supplementary). So $x=180^{\circ}- 129^{\circ}=51^{\circ}$

Answer:

$129$, $51$, $129$