Question

In the figure given below,LM=LN angle PLN=110 degree . Calculate : (i) angle LMN (ii) angle MLN​

Answer 1

Given : in given figure LM=LN angle PLN=110 degree

To find : (i) angle LMN (ii) angle MLN​

Solution:

in Quadrilateral PLNQ

∠PLN + ∠LNQ  + ∠NQP + ∠QPL = 360°

=> 110° + ∠LNQ + 90° + 90° = 360°

=>  ∠LNQ = 70°

∠LNM = ∠LNQ   ∵ M lies on NQ

=> ∠LNM =  70°

∠LMN = ∠LNM      ∵ LM = LN

=> ∠LMN =    70°

∠LMN + ∠LNM  + ∠MLN  = 180°

=> 70° + 70°  +  ∠MLN  = 180°

=> ∠MLN  = 40°

∠LMN =    70°

∠MLN  = 40°

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