Answer:
∠ LMN = 80°
Step-by-step explanation:
In a parallelogram
• consecutive angles are supplementary ( sum to 180° )
∠ MLQ and ∠ NQL are consecutive angles , then
∠ LQM + ∠ MQN + ∠ MLQ = 180° , that is
∠ LQM + 29° + 100° = 180°
∠ LQM + 129° = 180° ( subtract 129° from both sides )
∠ LQM = 51°
Then ∠ LQN = ∠ LQM + ∠ MQN = 51° + 29° = 80°
In a parallelogram
• opposite angles are congruent (equal ) , then
∠ LMN = ∠ LQN = 80°
