Question

the diagonals of a rectangle PQRS intersect each other at O. If ∠ROQ = 40o , find the measure of ∠OPS.

Answer 1

if ∠ROQ is 40 then ∠SOP is also 40
(vertically opposite)

therefore by isosceles triangle property (diagonals of rectangle are equal)

180=2x+40
2x=180-40
x=140/2=70
therefore ∠OPS=70 degree

Answer 2

∠OPS  = 70° if the diagonals of a rectangle PQRS intersect each other at O. and ∠ROQ = 40°

Step-by-step explanation:

the diagonals of a rectangle PQRS intersect each other at O

Diagonal of rectangle bisect each other

and diagonal of rectangle are equal

=> PO = RO = QO = SO

∠ROQ = 40°

∠POS = ∠ROQ ( opposite angles)

=> ∠POS = 40°

in Δ POS

PO = SO

=> ∠OPS = ∠OSP

∠OPS +  ∠OSP + ∠POS = 180°   ( sum of angles of triangle)

=> 2  ∠OPS  + 40° = 180°

=> 2  ∠OPS  = 140°

=>  ∠OPS  = 70°

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