In the trapezium MHRK, MK – a larger base. Straight lines MH and PK intersect at point E

In the trapezium MHRK, MK – a larger base. Straight lines MH and PK intersect at point E, angle MEK = 80 °, angle EHP = 40 °. Find the corners of the trapezoid.

Decision:

1. Since MНРK is a trapezoid, then HP is parallel to MK, therefore, the angle EHP = angle EMK = 40 ° (corresponding, since HP is parallel to MK, secant EM).

2. The angles of the КНP and MHР are adjacent, therefore, the angle MHР = 180 ° – 40 ° = 140 °.

3. Consider a triangle HEP: angle EHP = 40 °, angle HEP = 80 °;

Therefore, the angle EPH = 180 ° – (40 ° + 80 °) = 60 °.

4. Angle ЕРН = angle ЕКМ = 60 ° (corresponding, since НР is parallel to MK, secant ЕК).

5. The angles EPH and НРK are adjacent, therefore, the angle НРK = 180 ° – 60 ° = 120 °.