#### Answer

a) y=7
b) RS=60, ST=36, RT=96

#### Work Step by Step

According to the Segment Addition Postulate, $RS+ST=RT$. We substitute the values of RS, ST, and RT into the equation to get :$8y+4+4y+8=15y-9$. Combining like terms gives:
$$12y+12=15y-9 \\ -3y=-21 \\ y=7$$.
To find RS, ST, and RT, we substitute 7 in for any occurrence of y.
For RS, $8y+4=8(7)+4=56+4=60$.
For ST, $4y+8=4(7)+8=28+8=36$.
For RT, $15y-9=15(7)-9=105-9=96$