Question

first, find ( mangle khl ).
( mangle khl=)
now, find ( mangle lhm ).
( mangle lhm=)
finally, find ( mangle mhj ).
( mangle mhj=)
( mangle mhj = 180^{circ}-mangle lhm )

Explanation:

Step1: Find \(m\angle KHL\)

By observing the figure, \(m\angle KHL = 129^{\circ}\) (given directly in the problem statement).

Step2: Find \(m\angle LHM\)

Vertical angles are equal. The angle of \(51^{\circ}\) and \(\angle LHM\) are vertical angles. So \(m\angle LHM=51^{\circ}\)

Step3: Find \(m\angle MHJ\)

Since \(\angle MHJ\) and \(\angle LHM\) are supplementary (they form a linear - pair, \(m\angle MHJ + m\angle LHM=180^{\circ}\)). Substitute \(m\angle LHM = 51^{\circ}\) into the equation: \(m\angle MHJ=180 - 51\)

Answer:

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