Answer:
The length of TU is 8 units.
Step-by-step explanation:
In triangle XST and triangle XUT,
[tex]\angle SXT=\angle UXT[/tex] (Given)
[tex]\angle XST=\angle XUT=90^{\circ}[/tex] (Given)
[tex]\angle XT=\angle XT[/tex] (Common side)
By AAS postulate,
[tex]\triangle XST\cong \triangle XUT[/tex]
Now,
[tex]\angle ST=\angle UT[/tex] (CPCTC)
[tex]3x+2=7x-6[/tex]
[tex]8=4x[/tex]
[tex]2=x[/tex]
The value of x is 2.
[tex]TU=7x-6[/tex]
[tex]TU=7(2)-6[/tex]
[tex]TU=8[/tex]
Therefore the length of TU is 8 units.
