Question

7. Which is longer?
LM or MN (with reason)​

Answer 1

From the figure, LM = LN

So, ∠LMN = ∠MNL = 58° (Angles opposite to equal sides are equal)

By angle sum property,

∠LMN + ∠LNM + ∠MLN = 180°

58° + 58° + ∠MLN = 180°

116° + ∠MLN = 180°

∠MLN = 180° - 116°

∠MLN = 64°

So, we can say that ∠MLN > ∠MNL

We know, Sides opposite to larger angles are longer in length..

Therefore, MN is longer than LM

Hence Proved!

Hope this helps! Thank you!