∠LMN is 80°.
The total interior angle of a quadrilateral (such as parallelogram) is always 360°. Since ∠MLQ is congruent to ∠MNQ, so ∠MLQ = ∠MNQ = 100°. Also ∠LMN is congruent to ∠LQN.
Form an equation to solve for ∠LMN.
∠MLQ + ∠LMN + ∠MNQ + ∠LQN = 360°
2 ∠MLQ + 2 ∠LMN = 360°
2 (100°) + 2 ∠LMN = 360°
200° + 2 ∠LMN = 360°
2 ∠LMN = 360° - 200°
2 ∠LMN = 160°
∠LMN = 160°/2
∠LMN = 80°
