Rays PQ and QR are perpindicular. Point S lies i the interior of angle PQR. If the measure of the angle SQR=4+7a and the measure of angle SQR=9=4a, find the measure of angle of PQS and angle SQR.

Answer 1

angle PQS + angle PQR= 90
so, 4+7a+9+4a=90
7a+4a=90-4-9
11a=77
a=7

check:
PQS= 4+7a
4+7(7)=53

PQR= 9+4a
=9+4(a)=37

53+37=90

Answer 2

angle PQS + angle SQR= 90
so, 4+7a+9+4a=90
7a+4a=90-4-9
11a=77
a=7

check:
PQS= 4+7a
4+7(7)=53

SQR= 9+4a
=9+4(a)=37

53+37=90