Answer:
[tex]\angle PQR=30^{\circ}[/tex]
Step-by-step explanation:
It is given that,
[tex]\angle PQS=16^{\circ}\\\\\angle SQR=(9x+17)^{\circ}\\\\\angle PQR=(12x-6)^{\circ}[/tex]
We need to find the measure of [tex]\angle PQR[/tex].
From the given figure, [tex]\angle PQR=\angle PQS+\angle SQR[/tex]
Putting all the values, we get :
[tex]12x-6=16+9x+17\\\\12x-9x=16+17+6\\\\3x=39\\\\x=13[/tex]
[tex]\angle PQR=12x-6\\\\=12(3)-6\\\\=30^{\circ}[/tex]
So, the measure of [tex]\angle PQR[/tex] is 30 degrees.
