Answer: [tex]\angle STU=34^{\circ}, \angle TVW=116^{\circ}[/tex]
Step-by-step explanation:
By the alternate interior angles theorem,
[tex]3x+4=2x+14\\\\x+4=14\\\\x=10\\\\\implies \angle STU=3(10)+4=\boxed{34^{\circ}}[/tex]
By the alternate interior angles theorem, [tex]\angle UTV=82^{\circ}[/tex], and we also know that [tex]\angle TUV=34^{\circ}[/tex].
Thus, by the exterior angle theorem,
[tex]\angle TVW=82+34=\boxed{116^{\circ}}[/tex]
