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Question

# In figure, PQRS is a rectangle. If ∠RPQ=30∘ then the value of (x+y) is

A
90
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B
120
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C
150
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D
180
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Solution

## The correct option is D 180∘Let the point of intersection of the diagonals of the rectangle be O.Given ∠OPQ=30°∴∠SPO=60° Similarly ∠RQO=60°As its a rectangle, all the angles are 90°.∴∠PQR=∠PQO+∠OQR =30°+60° =90°∴∠OQR=60° i.e, x=60°From △POQSum of angles of △les =180°⇒∠OPQ+∠PQO+∠POQ=180°∴∠POQ=180°−30o−30o=120°i.e, ∠POQ=∠SOR=120°=y [ i.e, opposite angles ]∴ Sum of x+y=120°+60°=180°.Hence, the answer is 180°.

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