PQRS is a rectangle.
∴ PM = (1/2) PR …(i)
MS = (1/2) QS …(ii) [Diagonals of a rectangle bisect each other]
Also, PR = QS …..(iii) [Diagonals of a rectangle are congruent]
∴ PM = MS ….(iv) [From (i), (ii) and (iii)]
In ∆PMS, PM = MS [From (iv)]
∴ ∠MSP = ∠MPS = x° …..(v) [Isosceles triangle theorem]
∠PMS = ∠QMR = 50° ……(vi) [Vertically opposite angles]
In ∆MPS, ∠PMS + ∠MPS + ∠MSP = 180° [Sum of the measures of the angles of a triangle is 180°]
∴ 50° + x + x = 180° [From (v) and (vi)]
∴ 50° + 2x = 180°
∴ 2x= 180° - 50°
∴ 2x = 130°
∴ x = 130/2 = 65°
∴ ∠MPS = 65° [From (v)]
