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Question

# In the given 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∘ We know that, the diagonals of a rectangle bisect each other ⇒ OP = OQ = OR = OS Given, ∠RPQ=∠OPQ=30∘ Since, OP=OQ, ∠OPQ=∠OQP=30∘ All the angles of a rectangle are 90∘. x=90∘−∠OQP=90∘−30∘=60∘ Also, ∠POQ=∠SOR=y (Vertically Opposite Angles) ⇒y=180∘−(∠OPQ+∠OQP) ⇒y=180∘−60∘=120∘ Hence, the required sum is, x+y=60∘+120∘=180∘

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