In Fig. 6.1, if AB || CD || EF, PQ || RS, ∠RQD = 25° and ∠CQP = 60°, then ∠QRS is equal to
a) 85°
b) 135°
c) 145°
d) 110°

Solution:

The figure represents a pair of lines cut by transversal

Given, the line segments AB || CD || EF

The transversal PQ || RS

Given, ∠RQD = 25° and ∠CQP = 60°

We have to find the measure of ∠QRS.

We know that, if a transversal intersects two or more parallel lines, then the alternate interior angles are equal.

Given, ∠RQD = 25°

From the figure, the equal alternate interior angles are

∠RQD = ∠QRA

So, ∠QRA = 25°

We know that, if a transversal intersects two or more parallel lines, then the alternate exterior angles are equal.

Given, exterior angle ∠CQP = 60°

From the figure, the equal alternate interior angles are

∠CQP = ∠SRB

So, ∠SRB = 60°

From the figure,

∠QRS = ∠QRA + ∠SRA

From the figure, ∠SRA = 180° - ∠SRB

∠SRA = 180° - 60°

∠SRA = 120°

Now, ∠QRS = 25° + 120°

Therefore, ∠QRS = 145°

✦ Try This: Can two obtuse angles form a linear pair?

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 6

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NCERT Exemplar Class 9 Maths Exercise 6.1 Problem 1

In Fig. 6.1, if AB || CD || EF, PQ || RS, ∠RQD = 25° and ∠CQP = 60°, then ∠QRS is equal to a) 85°, b) 135°, c) 145°, d) 110°

Summary:

The figure represents parallel lines cut by a transversal, if AB || CD || EF, PQ || RS, ∠RQD = 25° and ∠CQP = 60°, then ∠QRS is equal to 145°

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