RS=5y+5,ST=2y+4,and RT=51
A.what is the value of y

The properties of the incenter of a triangle are the following:
The center of the incircle wherein the incenter is the center of the triangle'sincircle, the largest circle that will fit inside the triangle and touch all three sides.
It is always inside the triangle. The triangle's incenter is always inside the triangle. Moving the triangle above by dragging any vertex and notice that it will never go outside the triangle.