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Vertically Opposite Angles

Two lines PQ ...

Question

Two lines PQ and LM intersect each other at a point O. Now, if the sum of ∠QOL and ∠MOP is 280^o, then ∠MOQ will be equal to

50^o

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60^o

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75^o

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40^o

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Solution

The correct option is D
40^o

∠QOL = ∠MOP (vertically opposite angles are equal)

∠QOL + ∠MOP =280^o

Hence ∠MOP = 140^o.

∠MOP + ∠MOQ = 180^o (linear pair)

Substituting the value of ∠MOP

∠MOQ = 40^o

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