Question

If ABC is an isosceles triangle in which AB=AC and LM is parallel to BC. If LA=60° find LMC.​

Answer 1

REF.Image.

Given △ABC is isosceles △ with AB=AC

LM∥BC & ∠A=50  

∘

 

If △ABC is isosceles then ∠B=∠C

∠A+∠B+∠C=180  

∘

 

50  

∘

+2∠B=180

2∠B=180−50  

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∠B=  

2

130

​

 

∠B=65  

∘

=∠C

Now ∠MCB=∠AML(∴ cooreponding ∠ b/w two || lines)

50  

∘

⇒65  

∘

=∠AML...(1)

Now at point M∠AMC=180  

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∠AML+∠LMC=180  

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  (∴∠AMC=∠AML+∠LMC)

from (1)

65  

∘

+∠LMC=180  

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∠LMC=180  

∘

−65  

∘

 

∠LMC=115  

∘

 

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