Question

HELLLLLLLLPPPP The value of x is

Answer 1

Angle QRT is an exterior angle to the triangle.  The rule is that the exterior angle of a triangle is equal to the sum of its remote interior angles.  Those remote interior angles are angle RTS and angle TSR.  So our equation is $9x=(5x)+(9+x)$.  We can remove the parenthesis and simplify by combining like terms to get 9x = 5x + 9 + x and 9x = 6x + 9 and 3x = 9.  That means that x = 3.