Question

line jl and line km intersect at point h. find the three unknown angle measures in the figure. first, find m∠khl. m∠khl = 129 now, find m∠lhm. m∠lhm = 51 finally, find m∠mij. m∠mij = 51 m∠mij = 180 - m∠lhm

Explanation:

Step1: Find $m\angle KHL$

Vertical - angles are equal. $\angle KHL$ and the given $129^{\circ}$ angle are vertical - angles, so $m\angle KHL = 129^{\circ}$.

Step2: Find $m\angle LHM$

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

Step3: Find $m\angle MHJ$

$\angle MHJ$ and $\angle LHM$ are supplementary (a linear pair). Since $\angle MHJ=180^{\circ}-m\angle LHM$ and $m\angle LHM = 51^{\circ}$, then $m\angle MHJ = 180 - 51=51^{\circ}$.

Answer:

$m\angle KHL = 129^{\circ}$, $m\angle LHM=51^{\circ}$, $m\angle MHJ = 51^{\circ}$