Question

Points P,Q and S are Collinear a) What is m

Answer 1

Given Points P, Q, and S are collinear

m∠ PQR = 3x - 5

m∠ SQR = x + 1

m∠ PQR + m∠ SQR = 180

So,

$\begin{gathered} 3x-5+x+1=180 \\ 4x-4=180 \\ 4x=180+4 \\ 4x=184 \\ x=\frac{184}{4}=46 \end{gathered}$

Substitute with x to find m∠ PQR

So,

$m\angle\text{PQR}=3x-5=3\cdot46-5=133\degree$

b) Ray QT bisects m∠RQS

So, m∠RQS = x + 1 = 46 + 1 = 47

The measure of one of the resulting angles =

$\frac{m\angle RQS}{2}=\frac{47}{2}=23.5\degree$