Question

In figure, if and , then is equal to:

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A

B

C

D

Medium

Solution

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Correct option is
C

Using the fact that OP || RS, we know that
∠RWV = 180° − 130°
1.  ∠RWV = 50° 

We know that,
∠PWQ = ∠RWV = 50° (Since, opposite angles of intersecting lines are equal)

Also, for line OP
∠OQP + θ = 180°
θ = 180° − ∠OPQ = 180° − 110°
2.  θ = 70°

Now, we know that sum of angles of a triangle is 180°,
∠PQR + θ + ∠PWQ = 180°
∠PQR = 180° − θ − ∠PWQ = 180° − 70° − 50°
∠PQR = 180° − 120°
∠PQR = 60°

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