Answer:
• x=7
,• m∠TSU =89 degrees
Explanation:
From the diagram:
Angles STU and TUS are opposite interior angles of angle TSW.
We know that 'the sum of the two opposite interior angles is equal to the exterior angle'.
Therefore:
[tex]m\angle\text{TSW}=m\angle STU+m\angle\text{TUS}[/tex]Substituting the given values, we have:
[tex]\begin{gathered} 12x+7=5x-1+57^0 \\ 12x-5x=57-1-7 \\ 7x=49 \\ x=\frac{49}{7} \\ x=7 \end{gathered}[/tex]The value of x is 7.
Angles TSW and TSU are linear pairs. First, we find the value of TSW.
[tex]\begin{gathered} \angle\text{TSW}=12x+7 \\ =12(7)+7 \\ =84+7 \\ =91^0 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} m\angle\text{TSU}=180-91 \\ =89^0 \end{gathered}[/tex]