If a ray QT bisects <RQS, then [tex]m<TQS=23.5[/tex] °
Given :
a ray QT bisects <RQS
<PQR and <RQS is a linear pair . It makes and angle 180 degree
[tex]m<PQR+m<RQS=180[/tex]
From the diagram,
m<PQR=3x-5, and m<RQS=x+1
Substitute the expression and solve for x
[tex]m<PQR+m<RQS=180\\3x-5+x+1=180\\4x-4=180\\4x=180+4\\4x=184\\Divide \; by \; 4\\x=46[/tex]
now , [tex]m<RQS = x+1 =46+1=47[/tex]
Given QT bisects <RQS. it means QT divides RQS equally
[tex]m<TQS= \frac{m<RQS}{2} \\m<TQS= \frac{47}{2} \\\\m<TQS=23.5[/tex]
Learn more : brainly.com/question/16926292
