Step-by-step explanation:
The angles (8x + 28) and (4x - 7) are supplementary to each other so we can write
[tex](8x + 28) + (4x - 7) = 180 \Rightarrow 12x + 21 = 180[/tex]
or
[tex]x = 13.25[/tex]
Also, note that the angle (4x - 7) and [tex]\angle{TQS}[/tex] are vertical angles, which means that they are equal to each other. Therefore,
[tex]\angle{TQS} = 4x - 7 = 4(13.25) - 7 = 46°[/tex]
