Answer:
x=67 degrees
Step-by-step explanation:
Same side interior angles are 180 degrees.
<PNL+54=180
<PNL=180-54
<PNL=126
Since |PN|=|NL|
2<PLN+126=180
2<PLN=180-126
2<PLN=54
<PLN=27
Angles on a straight line add up to 180
<PLN+<MLQ+70=180
27+<MLQ+70=180
<MLQ+97=180
<MLQ=180-97
<MLQ=83
<MQL+54+83=180----> sum of interior angles in triangle MQL is 180.
<MQL+137=180
<MQL=180-137
<MQL=43
But <MQL=43=<PQL ---> it was given that QL bisects ∠PQM
Now x+70+43=180----> sum of angles in triangle PQL
[tex]x=180-70-43[/tex]
[tex]x=67\degree[/tex]
