The MHPK MK trapezoid has a larger base. Lines MH and PK intersect at point E, angle MEK = 80

The MHPK MK trapezoid has a larger base. Lines MH and PK intersect at point E, angle MEK = 80 °, angle EHP = 40 °. Find the corners of the trapezoid

Consider a triangle HEP, in which HEP = 800, ∠ENR = 400, then EPH = 180 – 80 – 40 = 60.

The angle of the NMC trapezoid is equal to the angle ЕНР of the triangle, as are the corresponding angles at the intersection of the secant ЕМ parallel lines MK and НР. ∠HMR = ∠ENR = 40.

The angle of the RKM trapezoid is equal to the angle of the ERN of the triangle, as are the corresponding angles at the intersection of the secant KE of the parallel lines MK and HP. ∠РКМ = ∠ЕРН = 60.

∠MNE – unfolded angle and is equal to 180, then ∠MNR = ∠MNE – ∠ENR = 180 – 40 = 140.

∠KRE – unfolded angle and is equal to 180, then ∠NRK = ∠KRE – ∠ERN = 180 – 60 = 120.

Answer: The angles of the trapezoid are equal: ∠НМР = 40, ∠РКМ = 60, ∠МНР = 1400, ∠НРК = 120.