Question

the figure PQRS is a square ∠PQM =27° and ∠NQR=22° find ∠MQN

Answer 1

the answer is in the above page

Answer 2

Step-by-step explanation:

Given: ZQPR = <PQR and M and N are respectively points on side QR and PR of

APQR, such that QM = PN. To Prove: OP = OQ, where O is the point of

intersection of PM and QN.

Proof: In APNQ and AQMP,

PN = QM | Given

PQ = QP | Common

ZQPN = <PQM | Given

:: ΔΡΝΟ = ΔΩΜΡ

| SAS congruence rule :: ZPNQ = ZQMP | CPCT

Again, in ΔΡΝΟ and ΔΩΜΟ,

PN = QM | Given ZPON=ZQOM

| Vertically opposite angles ZPNO = 2QMO | Proved above

:: ΔΡΝΟ = ΔΩΜΟ

| AAS congruence rule .. OP = OQ | CPCT