we know that
in the triangle PQR
m∠PQR+m∠QPR+m∠QRP=180°------> the sum of the internal angles of a triangle is equal to 180 degrees
(m∠PQR+m∠QRP)+74°=180°-------> (m∠PQR+m∠QRP)=106°
we know that
If QS and SR are angle bisectors
then
In the triangle QSR
m∠SQR+m∠QSR+m∠QRS=180°-------> equation 1
and
(m∠SQR+m∠QRS)=106°/2--------> (m∠SQR+m∠QRS)=53°
substitute the value of (m∠SQR+m∠QRS)=53° in the equation 1
53°+m∠QSR=180°
m∠QSR=180°-53°-------->m∠QSR= 27°
therefore
the answer is
The measure of angle QSR is 27 degrees
