Okay, here we have this:
Considering the provided information, we obtain the following:
m∠KJM:
As in an isosceles triangle the base angles are the same, we have:
m∠KJM=m∠LMJ
m∠KJM=27°+78°
m∠KJM=105°
m∠JKL:
Now, as in isosceles triangle opposite angles are supplementary we obtain:
180°=m∠JKL+m∠LMJ
m∠JKL=180°-m∠LMJ
m∠JKL=180°-(27°+78°)
m∠JKL=180°-(105°)
m∠JKL=75°
JL:
In this case, considering that as the diagonals are the same length, this mean that KR is equal to RL, so RL measures 42 units, and we have:
JL=JR+RL
JL=39+42
JL=81
LM:
Finally we