Answer:
[tex]x=38[/tex]
Step-by-step explanation:
[tex]We\ are\ given\ that,\\\angle KLO=134\\\angle OMN= 84\\Hence\ we\ observe\ that,\\\angle KLO\ and\ \angle OLM\ form\ a\ linear\ pair\ and\ hence,\ are\ supplementary.\\Hence,\\\angle KLO\ + \angle OLM=180\\Substituting\ \angle KLO=134,\\134+\angle OLM=180\\\angle OLM=180-134\\\angle OLM=46\\Similarly,[/tex]
[tex]\angle OMN\ and\ \angle OML\ form\ a\ linear\ pair\ and\ hence,\ are\ supplementary.\\Hence,\\\angle OMN\ + \angle OML=180\\Substituting\ \angle OMN=84,\\84+\angle OLM=180\\\angle OLM=180-84\\\angle OLM=96\\[/tex]
[tex]Now\ lets\ consider\ \triangle OML,\\\angle OLM + \angle OML+ \angle LOM=180 [Angle\ Sum\ Property\ Of\ a\ triangle]\\Hence\ substituting\ \angle OLM=46, \angle OML=96, \angle LOM=x\\46+96+x=180\\142+x=180\\x=180-142\\x=38[/tex]
