Answer:
28°
Step-by-step explanation:
[tex]m\angle UVI +m\angle IVW =m\angle UVW[/tex]
(By angle sum postulate)
[tex]\implies (3x+7)\degree +(12x+6)\degree =118\degree[/tex]
[tex]\implies (15x+13)\degree =118\degree[/tex]
[tex]\implies 15x+13 =118[/tex]
[tex]\implies 15x =118-13[/tex]
[tex]\implies 15x =105[/tex]
[tex]\implies x =\frac{105}{15}[/tex]
[tex]\implies x =7[/tex]
[tex]m\angle UVI =(3x+7)\degree[/tex]
[tex]\implies m\angle UVI =(3*7+7)\degree[/tex]
[tex]\implies m\angle UVI =28\degree[/tex]
