Question

In △ LMN, ∠L+∠M=110° and ∠N+∠M=128° the values of ∠M, ∠L and ∠N are ...

Answer 1

Answer:

∠L = 52°, ∠M = 58° and ∠N = 70°

Step-by-step explanation:

Given that ∠L + ∠M = 110° --- (i)

and  ∠N + ∠M = 128° --- (ii)

Adding both equations

∠L + ∠M + ∠N + ∠M = 110° + 128°

[∵ According to Angle Sum Property of Triangle  ∠L + ∠M + ∠N = 180° ]

180° + ∠M = 238°    

∠M = 238° - 180°

∠M = 58°

Putting value in (i) and (ii)

∠L + ∠M = 110°        ∠N + ∠M = 128°

∠L + 58° = 110°        ∠N + 58° = 128°

∠L  = 110° - 58°         ∠N = 128° - 58°

∠L  = 52°                  ∠N  = 70°

Hence, ∠L = 52°, ∠M = 58° and ∠N = 70°