Question

PQRSis a parllelogram whoms diagnols intersect a M if PMS=66degree find qmr​

Answer 1

Given : ||gm PQRS in which diagonals PR & QS intersect at M.  ∠PMS = 54° ; ∠QSR = 25° and ∠SQR=30° To find : (i) ∠RPS (ii) ∠PRS (iii) ∠PSR  Proof : QR || PS => ∠PSQ = ∠SQR (Alternate ∠s)  But ∠SQR = 30° (Given)  ∠PSQ = 30°  In ΔSMP, ∠PMS + ∠ PSM +∠MPS = 180° or 54° + 30° + ∠RPS = 180°  ∠RPS = 180°- 84° = 96°  Now ∠PRS + ∠RSQ = ∠PMS  ∠PRS + 25° =54°  ∠PRS = 54° – 25° = 29°  ∠PSR = ∠PSQ + ∠RSQ = 30°+25° = 55°  Hence (i) ∠RPS = 96° (ii) ∠PRS = 29° (iii) ∠PSR = 55°