IN the given figure LM PARALLEL TO NQ. FIND the value of X.

Extend RQ such that it meets LM at P
 
In triangle PMRPMR+MRQ+RPM=180°  Angle sum propertyx+30+RPM=180°RPM=150°-xAs, PQR is straight lineRQN+PQN=180°   Linear pairPQN=180°-140°=40°Now we are given that LM is parallel to NQRPM=PQN Alternate interior angles150°-x=40°x=150°-40°x=110°    

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extend NQ as an imaginary line to mr at point t such that NT is parallel to LM
now, angle RQT= 180-140=40
In triangle QTR 40+30+x=180
x=110 as angle m is equal to angle t
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