Given Points P, Q, and S are collinear
m∠ PQR = 3x - 5
m∠ SQR = x + 1
m∠ PQR + m∠ SQR = 180
So,
[tex]\begin{gathered} 3x-5+x+1=180 \\ 4x-4=180 \\ 4x=180+4 \\ 4x=184 \\ x=\frac{184}{4}=46 \end{gathered}[/tex]
Substitute with x to find m∠ PQR
So,
[tex]m\angle\text{PQR}=3x-5=3\cdot46-5=133\degree[/tex]
b) Ray QT bisects m∠RQS
So, m∠RQS = x + 1 = 46 + 1 = 47
The measure of one of the resulting angles =
[tex]\frac{m\angle RQS}{2}=\frac{47}{2}=23.5\degree[/tex]
