Question

diagonals of a rectangle pqrs are intersecting at point in n if angle q and r is equal to 50 degree then find the measures of angle mps

Answer 1

in a rectangle with two diagonals are of equal magnitude and make equal angles on the sides and the opposite sides are parallel and equal to each other

so, angle PSM = angle RQM (i) and angle SPM = angle QRM

In ∆SMP and ∆RMQ,
Angle PSM = Angle RQM (from i)
PS = QP. (opposite sides are equal)
Angle SMP = Angle RMQ. (each measure 50°)

so by ASA congruency criterion ∆SMP is congruent to ∆RMQ

So SM =QM and PM =RM
and the
magnitude of the rectangular same so,
SM=PM
so angleMSP = angleMPS

in ∆MSP,
anglePSM +angleMPS + angleSMP = 180° (angle sum property of triangle )

rectangle in MPS be x ,

x + x + 50° = 180° ( angle MPS = angle PSM)
2x = 180° - 50°
x = 130°/2
x = 65°

So angle MPS is equal to 65°