I'm not sure how to do this. I did however draw a diagram and measure the angle sizes.

Question

518.Let P = (−15,0), Q = (5,0), R = (8,21), and S = (0,15). Draw quadrilateral PQRS and measure its sides and angles. Is there anything remarkable about this figure?

RQP = 98 degrees

SPQ = 45 degrees

RSP = 171 degrees

SRQ = 45 degrees

Answer 1

The figure below shows the plotted points. The slopes were determined by the coordinates and evaluating the rise over the run.

               

RQP = 90º + tan-¹(1/7)

RQP = 98.13º

SPQ = tan^-1(1)

SPQ = 45º            

RSP = tan^-1(4/3) - tan^-1(1/7)

RSP = 45º              

SRQ = tan^-1(3/4) + 90 + tan^-1(1)

SRQ = 171.87º

The remarkable thing is that angle RSP matches angle SPQ and that tan^-1(4/3) - tan^-1(1/7) = 45º.