The value of x in the figure is 8/5.
What is angle bisector theorem?
As per the Angle bisector theorem, the ratio of the line segment RS to SP equals the ratio of the length of the side QR to QP.
PR = 40
PS = x
SR = PR - PS
= 40 - x
RS/SP = QR/QP
40 - x/x = 45/30
30(40 - x) = 45x
120 - 30x = 45x
120 = 30x + 45x
75x = 120
x = 120/75
x = 8/5
The value of x in the figure is 8/5.