ICSE-VIII-Mathematics
17: Special Types of Quadrilaterals Class 8 Maths
- #8PQRS is a parallelogram whose diagonals intersect at M.
If ∠PMS = 54°, ∠QSR = 25° and ∠SQR = 30° ; find : (i) ∠RPS (ii) ∠PRS (iii) ∠PSR.Ans : 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 ∆SMP,
∠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°