Dear Student , Please find below the solution to the asked query : ∠LMO=12 ∠LMN Since MO is the bisector of ∠LMN ∠LMO=12×54°=27°∠OMN=12 ∠LMN Since MO is the bisector of ∠LMN ∠OMN=12×54°=27°∠MLN+∠NLP=180° Linear Pair∠MLN+120°=180°∠MLN=60°∠LNM+∠MLN+∠LMN=180° Angle Sum Property∠LNM+60°+54°=180°∠LNM=180°-114°∠LNM=66°∠ONM=12 ∠LNM Since NO is the bisector of ∠LNM ∠ONM=12×66°=33°∠OMN+∠ONM+∠MON=180° Angle Sum Property27°+33°+∠MON=180°∠MON=180°-60°∠MON=120° Hope this information will clear your doubts about the topic If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible Regards

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Dear Student ,

Please find below the solution to the asked query :

∠ LMO = \frac{1}{2} ∠ LMN (Since MO is the bisector of ∠ LMN) ∠ LMO = \frac{1}{2} \times 54 ° = 27 ° ∠ OMN = \frac{1}{2} ∠ LMN (Since MO is the bisector of ∠ LMN) ∠ OMN = \frac{1}{2} \times 54 ° = 27 ° ∠ MLN + ∠ NLP = 180 ° (Linear Pair) ∠ MLN + 120 ° = 180 ° ∠ MLN = 60 ° ∠ LNM + ∠ MLN + ∠ LMN = 180 ° (Angle Sum Property) ∠ LNM + 60 ° + 54 ° = 180 ° ∠ LNM = 180 ° - 114 ° ∠ LNM = 66 ° ∠ ONM = \frac{1}{2} ∠ LNM (Since NO is the bisector of ∠ LNM) ∠ ONM = \frac{1}{2} \times 66 ° = 33 ° ∠ OMN + ∠ ONM + ∠ MON = 180 ° (Angle Sum Property) 27 ° + 33 ° + ∠ MON = 180 ° ∠ MON = 180 ° - 60 ° ∠ MON = 120 °

Hope this information will clear your doubts about the topic .

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible .

Regards

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