Question

In the adjoining figure, ABC is an isosceles triangle with AB = AC and LM is parallel to BC. If ∠A = 50°, find ∠LMC.

Answer 1

Answer:

110° will be the angle

of ∠LMC

Answer 2

∠LMC  = 115∘

Explanation:

△ABC is isosceles.

AB=AC

LM∥BC  

∠A=50∘

In an isosceles triangle, base angles are equal, so ∠B = ∠C.

∠A + ∠B +∠C = 180∘

50∘ + 2∠B = 180∘

∠B  = 130∘ / 2 = 65∘

∠MCB = ∠AML as they are corresponding angles between two parallel lines.

So  ∠AML = ∠C = 65∘

∠LMC = 180∘ - ∠AML (lie on a straight line).

=  180∘ - 65∘

∠LMC  = 115∘