Question

In figure, if $OP\parallel RS,\angle OPQ={110}^o$ and $\angle QRS={130}^o$, then $\angle PQR$ is equal to:

• A. ${40}^o$
• B. ${50}^o$
• C. ${60}^o$
• D. ${70}^o$

Answer 1

Answer: (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°