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Q is the incenter of the triangle, which means that it has the same distance to the three sides of the triangle. QM, QP, and QN are line segments perpedicular to the sides and so their measure indicates that distance. So PQ must also be 6 units long.

LQ is an angle bisecto, so the measure of PLN is 2(22)= 44 degrees.

Measure of PJM is 180-(44+ 34) = 102 degrees, so PJQ has measure (1/2)(102) = 51 degrees since JQ is an angle bisector.

Guest Feb 7, 2021