Mathematics

# In the adjoin figure, $ABC$ is an isocules triangle with $AB=AC$ & $LM$ is parallel to $BC$. If $\angle A=50^o$, find $\angle LMC$.

##### SOLUTION
REF.Image.
Given $\triangle ABC$ is isosceles $\triangle$ with $AB = AC$
$LM \parallel BC$ & $\angle A = 50^{\circ}$
If $\triangle ABC$ is isosceles then $\angle B = \angle C$
$\angle A + \angle B + \angle C = 180^{\circ}$
$50^{\circ} + 2\angle B = 180$
$2\angle B = 180 -50^{\circ}$
$\angle B = \dfrac{130}{2}$
$\angle B = 65^{\circ} = \angle C$
Now $\angle MCB = \angle AML (\therefore$ cooreponding $\angle$ b/w two || lines)
$50^{\circ} \Rightarrow 65^{\circ} = \angle AML ...(1)$
Now at point $M \angle AMC = 180^{\circ}$
$\angle AML + \angle LMC = 180^{\circ}$  $(\therefore \angle AMC = \angle AML +\angle LMC)$
from (1)
$65^{\circ}+ \angle LMC = 180^{\circ}$
$\angle LMC = 180^{\circ}-65^{\circ}$
$\boxed{\angle LMC = 115^{\circ}}$

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Subjective Medium Published on 09th 09, 2020
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