Due to Similar angles on two parallel lines, Angle ABC = Angle APQ & Angle PAQ = Angle CAB due to Similar angle
In triangle BPS, which is a rt angle triangle Angle PBS + Angle BSP + Angle SPB = 180 & Angle PBS = Angle ABC similar angles
Angle PBS = 90 - Angle ABC
Since straight line is formed by points BPA, Angle PBS + 90 + Angle APQ = 180
Use the above equations to solve and get the value of angle. Then using sin or cos functions get the value of length BS and length PS. The dimensions of rectangle can be used to calculate the area which can be subtracted from area of triangle ABC
Answers & Comments
Angle APQ + Angle AQP + Angle PAQ = 180 & Angle APQ = Angle AQP
In triangle ABC,
Angle ABC + Angle BCA + Angle CAB = 180 & Angle ABC = Angle BCA
Due to Similar angles on two parallel lines, Angle ABC = Angle APQ & Angle PAQ = Angle CAB due to Similar angle
In triangle BPS, which is a rt angle triangle
Angle PBS + Angle BSP + Angle SPB = 180 & Angle PBS = Angle ABC similar angles
Angle PBS = 90 - Angle ABC
Since straight line is formed by points BPA,
Angle PBS + 90 + Angle APQ = 180
Use the above equations to solve and get the value of angle. Then using sin or cos functions get the value of length BS and length PS. The dimensions of rectangle can be used to calculate the area which can be subtracted from area of triangle ABC