Question

Diagonals of a rectangle PQRS are intersecting in point M. If ∠QMR=50° then find the measure of ∠MPS.

Answer 1

If ∠QMR=50° then ∠SMP is also 50°
(vertically opposite)
So, By using isosceles triangle property (diagonals of rectangle are equal)

180=2x+50
2x=180-50
x=130/2=65

Henceforth,∠MPS= 65 degree

Answer 2

Answer:

Diagonals of a rectangle PQRS are intersecting in point M. If ∠QMR=50° then  the measure of ∠MPS = 65°

Step-by-step explanation:

in Δ PMS

∠MPS + ∠MSP + ∠PSM = 180° ( sum of angles of a triangle)

∠PSM = ∠QMR  ( opposite angles)

=>∠PSM = 50°

∠MPS = ∠MSP  ( as diagonal of rectangle are equal & bisect at intersection points so MS = MP =>∠MPS = ∠MSP )

∠MPS + ∠MPS + 50°  = 180°

=> 2∠MPS  = 130°

=> ∠MPS = 65°