Question

Can someone help me with this?​

Answer 1

30°

Step-by-step explanation:

∠LMP + ∠PMN = 180°

[∠LMO + ∠OMP] + [∠PMR + ∠RMN] = 180°

FIND x

(x - 10) + (x + 30) + x + 40 = 180

3x - 10 + 30 + 40 = 180

3x + 60 = 180

3x = 120

x =40

FIND ∠LMO

∠LMO = x - 10

∠LMO = (40) - 10

∠LMO = 30°

Hope this helps and God bless!

Answer 2

∠LMO = 30°

Step-by-step explanation:

Angles on a straight line add up to 180°

⇒ (x - 10)° + (x + 30)° + 40° + x° = 180°

⇒ x° + x° + x° - 10° + 30° + 40° = 180°

⇒ 3x° + 60° = 180°

⇒ 3x° = 120°

⇒ x = 40

Substitute found value of x into the expression for ∠LMO:

⇒ ∠LMO = (40 - 10)°

⇒ ∠LMO = 30°