Answer:
x = 7 , y = 37
Step-by-step explanation:
For Δ LMN ≅ Δ PQR
Then corresponding angles must be congruent, that is
∠ P = ∠ L , substitute values
9x - 18 = 5x + 10 ( subtract 5x from both sides )
4x - 18 = 10 ( add 18 to both sides )
4x = 28 ( divide both sides by 4 )
x = 7
Then
∠ P = 9x - 18 = 9(7) - 18 = 63 - 18 = 45°
∠ R = 180° - (84 + 45)° ← sum of angles in a triangle = 180°
∠ R = 180° - 129° = 51°
Then ∠ N = ∠ R
2x + y = 51
2(7) + y = 51
14 + y = 51 ( subtract 14 from both sides )
y = 37