Question

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

Answer 1

Answer:

In the given rectangle PQRS,

∠QMR=∠PMS=50 …. (vertically opposite angles are equal)

Also, SQ=PR (Diagonals of a rectangle are equal)

So

SQ=1 /2=1/2PR

⇒SM=PM

⇒∠MSP=∠MPS (Angle opposite to equal sides are equal)

lnΔPMS

∠PMS+∠MSP+∠MPS=180 ∘

⇒50 ∘ +∠MPS+∠MPS=180

⇒2∠MPS=130

⇒∠MPS=65