Step-by-step explanation:
[tex]\overline{CA} + \overline{AT} = \overline{CT}[/tex]
Since A is the midpoint, then [tex]\overline{CA} = \overline{AT}.[/tex] Therefore, we can write
[tex]2x + 8 = 4x + 2 \Rightarrow x = 3[/tex]
Using this value for x, we can write
[tex]\overline{CT} = \overline{CA} + \overline{AT}[/tex]
[tex]\:\:\:\:\:\:\:\:= (2x + 8) + (4x + 2)[/tex]
[tex]\:\:\:\:\:\:\:\:= 2(3) + 8 + 4(3) + 2 = 28[/tex]
