/// identify the segment bisector, then find the length of sm, mt, and st.

The segment bisector is RM. The values of SM and MT are both 14 and the value of ST is 28.

To find all of these, you need to find x. You can find x by setting SM and MT equal to each other since they have been bisected.

x + 12 = 8x - 2 > add 2 to both sides

x + 14 = 8x ---> subtract x from both sides

14 = 7x > divide both sides by 7

2 = x

Now that we have x, we can solve all of these.

SM = x + 12

SM = 2 + 12

SM = 14

MT = 8x - 2

MT = 16 - 2

MT = 14

ST = SM + MT

ST = 14 + 14

ST = 28

The Segment bisector is the line with point R on it.

Before you can find the measurements of any of the segments, you must find the value of X. To do this follow these steps:

x+12=8x-2 (they are set equal to each other since they are cut by the bisector)

12=7x-2 (next, subtract X from each side and you get this)

14=7x (Add 2 to each side)

2=x (Divide both sides by 7)

Now that you know x=2, plug in 2 in all the places you see X in the equations.

To find SM:

x+12 (original equation)

2+12 (Plug in 2 for x)

14 (add 12 & 2)

To find MT:

8x-2 (original equation)

8(2)-2 (plug in 2 for X)

16-2 (multiply 8 & 2)

14 (subtract 16 &2)

There are 2 ways to find ST (you'll get the same answer)

1st way to find ST:

x+12+8x-2

2+12+8*2-2 (plug in 2 for X)

14+16-2 (add 12&2, multiply 8&2)

30-2 (Combine 14 &16)

28

2nd way to find ST:

14+14 (this is SM+MT)

28

Your final answers are:

The Segment bisector is the line with point R on it.

SM: 14

MT: 14

ST: 28

step-by-step explanation: