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Practise Class 7 Maths Chapter 5 MCQs Set 1 based on parallel lines, intersecting lines, vertically opposite angles, linear pairs, and perpendicular lines with detailed solutions.
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Chapter Information
- Class: 7
- Subject: Mathematics
- Chapter: 5 – Parallel and Intersecting Lines
- Practice Set: 1
- Board: CBSE
- Textbook Reference: NCERT Ganita Prakash
- Question Type: Multiple-Choice Questions (MCQs)
Introduction
Lines are an important part of geometry. They help us understand shapes, angles, patterns, and the arrangement of objects around us. Two lines may intersect at a point, remain parallel without meeting, or meet at a right angle.
In this practice set, students will explore intersecting lines, vertically opposite angles, linear pairs, and perpendicular lines through original multiple-choice questions with step-by-step explanations.
What Will You Learn?
After completing this practice set, students will be able to:
- Identify intersecting and parallel lines.
- Understand vertically opposite angles.
- Calculate an unknown angle using a linear pair.
- Recognise perpendicular lines.
- Apply basic angle properties to solve geometry problems.
Why Is This Topic Important?
Understanding the relationships between lines and angles builds a foundation for geometry. These concepts are useful when studying polygons, triangles, geometrical constructions, and more advanced angle relationships.
Exam Relevance
Questions from this topic may test students’ ability to:
- Identify different arrangements of lines.
- Apply the properties of angles formed by intersecting lines.
- Calculate unknown angles.
- Recognise right angles and perpendicular lines.
- Explain why certain angles are equal or add up to a particular value.
MCQs with Detailed Solutions
Question 1: Intersecting Lines
Two straight lines cross each other at a single point. What are these lines called?
A. Parallel lines
B. Intersecting lines
C. Curved lines
D. Line segments
Answer: B. Intersecting lines
Concept: Intersecting lines.
Explanation:
Two lines are called intersecting lines when they meet at a common point. The common point is called their point of intersection.
Parallel lines in the same plane do not meet, while curved lines are not straight lines.
Correct Answer: B. Intersecting lines
Question 2: Vertically Opposite Angles
Two straight lines intersect. One of the angles formed measures $$68^\circ$$. What is the measure of the angle directly opposite it?
A. $$22^\circ$$
B. $$68^\circ$$
C. $$112^\circ$$
D. $$180^\circ$$
Answer: B. $$68^\circ$$
Concept: Vertically opposite angles.
Explanation:
When two straight lines intersect, the angles directly opposite each other are called vertically opposite angles.
Vertically opposite angles are equal.
Therefore, if one angle measures $$68^\circ$$, the angle directly opposite it also measures:
$$68^\circ$$
Correct Answer: B. $$68^\circ$$
Question 3: Finding an Angle in a Linear Pair
Two adjacent angles form a straight line. If one angle measures $$125^\circ$$, what is the measure of the other angle?
A. $$45^\circ$$
B. $$55^\circ$$
C. $$65^\circ$$
D. $$125^\circ$$
Answer: B. $$55^\circ$$
Concept: Linear pair of angles.
Formula:
The sum of two angles forming a linear pair is:
$$\text{First angle}+\text{Second angle}=180^\circ$$
Solution:
Let the unknown angle be $$x$$.
Given:
$$125^\circ+x=180^\circ$$
Subtract $$125^\circ$$ from both sides:
$$x=180^\circ-125^\circ$$
$$x=55^\circ$$
Therefore, the other angle measures $$55^\circ$$.
Correct Answer: B. $$55^\circ$$
Question 4: Perpendicular Lines
Two straight lines intersect to form four right angles. What is the relationship between these lines?
A. They are parallel lines.
B. They are perpendicular lines.
C. They never meet.
D. They form only acute angles.
Answer: B. They are perpendicular lines.
Concept: Perpendicular lines.
Explanation:
Perpendicular lines intersect at right angles. Each right angle measures:
$$90^\circ$$
When two straight lines intersect perpendicularly, all four angles formed measure $$90^\circ$$.
Parallel lines do not intersect, so option A is incorrect.
Correct Answer: B. They are perpendicular lines.
Question 5: Identifying Parallel Lines
Which statement correctly describes two parallel straight lines in the same plane?
A. They meet at exactly one point.
B. They always intersect at right angles.
C. They never meet, even when extended indefinitely.
D. They always form an angle of $$45^\circ$$.
Answer: C. They never meet, even when extended indefinitely.
Concept: Parallel lines.
Explanation:
Parallel lines are straight lines in the same plane that remain the same distance apart and do not intersect, even when extended indefinitely.
Lines that intersect at right angles are perpendicular lines, not parallel lines.
Therefore, option C is correct.
Correct Answer: C. They never meet, even when extended indefinitely.
Important Formulas & Concepts
1. Vertically Opposite Angles
When two straight lines intersect, each pair of vertically opposite angles is equal.
For example:
$$\angle a=\angle c$$
$$\angle b=\angle d$$
Here, $$a$$ and $$c$$ represent one pair of vertically opposite angles, while $$b$$ and $$d$$ represent the other pair.
2. Linear Pair of Angles
Two adjacent angles forming a straight line add up to $$180^\circ$$.
$$\angle 1+\angle 2=180^\circ$$
3. Right Angle
A right angle measures:
$$90^\circ$$
4. Perpendicular Lines
Perpendicular lines intersect at right angles.
$$\text{Angle between perpendicular lines}=90^\circ$$
5. Parallel Lines
Parallel lines in the same plane do not intersect, even when extended indefinitely.
Related Practice Questions
Try solving these questions independently.
- What is the common point where two intersecting lines meet called?
- If one of two vertically opposite angles measures $$47^\circ$$, what is the measure of the other?
- Find the angle that forms a linear pair with an angle of $$96^\circ$$.
- How many right angles are formed when two perpendicular lines intersect?
- Can two parallel lines in the same plane intersect when extended indefinitely?
Mini Quiz Challenge
Question 1
What is the sum of the angles in a linear pair?
A. $$90^\circ$$
B. $$120^\circ$$
C. $$180^\circ$$
D. $$360^\circ$$
Answer: C. $$180^\circ$$
Question 2
If one angle is $$73^\circ$$, what is its vertically opposite angle?
A. $$17^\circ$$
B. $$73^\circ$$
C. $$107^\circ$$
D. $$180^\circ$$
Answer: B. $$73^\circ$$
Question 3
Which type of lines intersect at right angles?
A. Parallel lines
B. Perpendicular lines
C. Curved lines
D. Non-intersecting lines
Answer: B. Perpendicular lines
Exam Tips
- Remember that vertically opposite angles are equal.
- Use $$180^\circ$$ when solving linear-pair questions.
- A right angle always measures $$90^\circ$$.
- Do not confuse parallel lines with perpendicular lines.
- Write the calculation steps clearly when finding an unknown angle.
- Check that the final angle is reasonable and that all units are written correctly.
Quick Revision Notes
- Intersecting lines meet at a common point.
- Vertically opposite angles are equal.
- The angles in a linear pair add up to $$180^\circ$$.
- Perpendicular lines intersect at right angles.
- Parallel lines in the same plane never meet.
- A right angle measures $$90^\circ$$.
Common Mistakes Students Make
- Assuming vertically opposite angles add up to $$180^\circ$$ instead of being equal.
- Forgetting to subtract the known angle from $$180^\circ$$ when solving a linear pair.
- Confusing perpendicular lines with parallel lines.
- Treating every pair of intersecting lines as perpendicular.
- Forgetting to include the degree symbol in angle measurements.
Key Takeaways
The relationship between lines and angles is based on a few important geometric properties. Intersecting lines meet at a point, vertically opposite angles are equal, and a linear pair adds up to $$180^\circ$$. Perpendicular lines meet at right angles, while parallel lines in the same plane never intersect. Understanding these properties helps students solve geometry questions accurately.
FAQs
1. What are intersecting lines?
Intersecting lines are two lines that meet at a common point.
2. Are vertically opposite angles equal?
Yes. Vertically opposite angles formed by two intersecting straight lines are equal.
3. What is a linear pair?
A linear pair consists of two adjacent angles whose non-common arms form a straight line. Their sum is $$180^\circ$$.
4. What are perpendicular lines?
Perpendicular lines are lines that intersect at an angle of $$90^\circ$$.
5. What are parallel lines?
Parallel lines are straight lines in the same plane that never intersect, even when extended indefinitely.
Conclusion
This practice set introduces the basic relationships between parallel lines, intersecting lines, vertically opposite angles, linear pairs, and perpendicular lines. Practising these original MCQs and reviewing their explanations will help students strengthen their understanding of Class 7 Mathematics.
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