Answer:
x = 3, x = 11
Step-by-step explanation:
Since PR is an angle bisector then it divides the opposite side into segments which are proportional to the other 2 sides, that is
[tex]\frac{PQ}{PS}[/tex] = [tex]\frac{QR}{SR}[/tex] , substitute values
[tex]\frac{x+1}{16}[/tex] = [tex]\frac{x-2}{x+1}[/tex] ( cross- multiply )
(x + 1)(x + 1) = 16(x - 2) ← expand left side using FOIL
x² + 2x + 1 = 16x - 32 ( subtract 16x - 32 from both sides )
x² - 14x + 33 = 0 ← in standard form
(x - 3)(x - 11) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x - 11 = 0 ⇒ x = 11
