Question

please solve this question ​

Answer 1

Answer:

Refer to the attachment for the diagram.

Given:

• Δ ABC is an isosceles triangle such that AB = AC.
• LM ║ BC
• ∠ A = 60°

To Find:

• ∠ LMC = ?

Solution:

Since AB = BC, the angle opposite to these lines are also equal to each other. Therefore,

⇒ ∠B = ∠C

⇒ 60° + ∠B + ∠C = 180°

⇒ 2 ∠B = 180° - 60°

⇒ 2 ∠B = 120°

⇒ ∠B = 120/2 = 60° = ∠C

Therefore ∠B and ∠C are also 60°.

Now if we consider the line LM,

⇒ ∠ LMC + ∠ LMA = 180°  [ Supplementary Angles ]

We know that corresponding angles are equal.

⇒ ∠ LMA = ∠ C = 60°  [ Corresponding Angles ]

⇒ ∠ LMC = 180° - 60°

⇒ ∠ LMC = 120°

Therefore ∠ LMC is equal to 120°.

Hope it helped !!