Answer:
[tex] \boxed{m \angle UTS = 165 \degree} [/tex]
Given:
[tex] m \angle UTV = (x + 15) \degree \\ \\ m \angle VTS = 140 \degree \\ \\ m \angle UTS = (15x + 15)\degree [/tex]
Step-by-step explanation:
[tex]=> m \angle UTS = m \angle UTV + m \angle VTS \\ \\ = > (15x + 15) \degree = (x + 15)\degree + 140\degree \\ \\ = > 15x\degree + 15\degree = x\degree + 15\degree + 140\degree \\ \\ = > 15x\degree + (15\degree - 15\degree) = x\degree + (15\degree - 15\degree )+ 140\degree \\ \\ = > 15x\degree = x\degree + 140\degree \\ \\ = > (15x\degree - x\degree) = (x\degree - x\degree) + 140\degree \\ \\ = > 14x\degree = 140\degree \\ \\ = > \frac{ \cancel{14}x}{ \cancel{14}} \degree = \frac{140}{14} \degree \\ \\ = > x\degree = 10\degree \\ \\ \\ So, \\ = > m \angle UTS = (15x + 15)\degree \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =(15 \times 10 + 15)\degree \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =(150 + 15) \degree \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =165 \degree[/tex]
