Question

7. In a parallelogram PQRS, the diagonals bisect at M. If angle PMS =
and SOR= 30°, find: () angle RPS (ii) angle PRS (iii) angle PSR
540, ZQSR = 25​

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°Read more on Sarthaks.com - https://www.sarthaks.com/170437/pqrs-is-parallelogram-whose-diagonals-intersect-at-m-if-pms-54-qsr-25-and-sqr-30-find