Triangles ABC and ADC lie in different planes and have a common side AC. Point P is the midpoint of AD

Triangles ABC and ADC lie in different planes and have a common side AC. Point P is the midpoint of AD and K is the midpoint of DC. a) What is the relative position of straight lines РK and AB? b) What is the angle between straight lines РK and AB, if ABC = 40 ° and BCA = 80 °?

Since, according to the condition, point P is the middle of the ABP segment, and point K is the middle of the DС segment, then the РC segment is the middle line of the AСD triangle and is parallel to the AC segment. The segment AC and РK lie in the same plane and are parallel, and the segment BA intersects the AC, then AB and РK are crossing straight lines. In the ABC triangle, the angle BAC = 180 – ABC – ACB = 180 – 60 – 80 = 40.

Since the segments AC and РK are parallel and lie in the same plane, the angle between AB and РK is equal to the angle between AC and AB and is equal to 40.

Answer: Lines AB and РK are crossing, the angle between lines РK and AB is 40.