Find all the angles in the following figure.

Given: ∠DMP = 135°

We know by proposition 4,

∠LMC = ∠DMP = 135° (vertically opposite angles (V.O.A))

We know by proposition 1,

∠DMP + ∠DML = 180°

135° + ∠DML = 180°

∠DML = 180° - 135°

∠DML = 45°

∠LMC = ∠DML = 45° (vertically opposite angles (V.O.A))

∠BLQ = ∠DML = 45° (Corresponding angles)

∠ALM = ∠BLQ = 45° (vertically opposite angles (V.O.A))

We know by proposition 1,

∠ALM + ∠ALQ = 180°

45° + ∠ALQ = 180°

∠ALQ = 180° - 45°

∠ALQ = 135°

∠BLM = ∠ALQ = 135° (vertically opposite angles (V.O.A))