The diagonals of a rectangle PQRS intersects at O. If angle ROQ=60 degree, then find angle OSP.

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The diagonals of a rectangle PQRS intersects at O If angle
ROQ=60 degree, then find angle OSP

Varun Rawat · Accepted Answer

We know that, diagonals of a rectangle are equal
So, PR = QS   
1We know that diagonals of a rectangle bisect each other
So, OP = OR  and OQ = OS    
2From 1 and 2, we getOP = OQ = OR = OSNow, ∠POS= ∠QOR = 60°  Vertically opposite anglesIn ∆POS,    OP = OS Proved above⇒∠OSP = ∠OPS   Angles opposite to equal sides are equalNow, ∠POS + ∠OPS + ∠OSP = 180°  Angle sum property⇒60° + 2∠OSP = 180°⇒2∠OSP= 120°⇒∠OSP = 60°