Question

In figure, if OP || RS, angle OPQ = 110° and Angle QRS = 130°, then angle PQR is equal to-




​

Answer 1

If OP//RS

Then

ON//RS

RQ is a transversal:

In OPN

∠OPQ + ∠QPN = 108            

∴∠QPN = 180-110

QPN = 70°    ----- (1)

∠PNR = ∠NRS                                      

∠PNR = 130

∠PNR + ∠QNP = 180            

∠QNP = 50°   ---- (2)

In ΔPQN:

∠PQN + ∠PNQ + ∠QPN = 180                  

∠PQR = 180-50-70

∠PQR = 60°.

Hope it helps!

Answer 2

Answer:

∠PQR = 60°

Step-by-step explanation:

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°