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Practise Class 7 Maths Chapter 5 MCQs Set 5 on parallel lines, intersecting lines, angle relationships, and geometric reasoning with detailed answers and solutions
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Chapter Information
- Class: 7
- Subject: Mathematics
- Chapter: 5 – Parallel and Intersecting Lines
- Practice Set: 5
- Board: CBSE
- Textbook Reference: NCERT Ganita Prakash
- Question Type: Multiple-Choice Questions (MCQs)
Introduction
Parallel and intersecting lines are important concepts in geometry. They help us understand how lines are arranged and how angles are related when lines meet. These properties are useful for solving geometrical problems and calculating unknown angles.
This practice set includes original questions on parallel lines, perpendicular lines, angle relationships, and geometric reasoning. Each question includes an explanation to help students understand the concept.
What Will You Learn?
After completing this practice set, students will be able to:
- Distinguish between parallel and intersecting lines.
- Identify perpendicular lines.
- Calculate unknown angles using geometric properties.
- Understand angle relationships formed by intersecting lines.
- Apply basic reasoning to solve geometry problems.
Why Is This Topic Important?
Understanding the relationships between lines is essential for learning geometry. These concepts help students analyse shapes, recognise patterns, and solve problems involving angles and geometrical constructions.
Exam Relevance
Questions from this topic may involve:
- Identifying parallel lines.
- Recognising perpendicular lines.
- Calculating angles on a straight line.
- Using vertically opposite angle properties.
- Applying geometric reasoning to numerical questions.
MCQs with Detailed Solutions
Question 1: Identifying Parallel Lines
Which statement correctly describes parallel straight lines in the same plane?
A. They always meet at a right angle.
B. They meet at exactly one point.
C. They remain the same distance apart and never meet.
D. They always form an acute angle.
Answer: C. They remain the same distance apart and never meet.
Concept: Parallel lines.
Explanation:
Parallel lines in the same plane remain the same distance apart and do not intersect, even when extended indefinitely.
Lines that meet at a point are intersecting lines. Lines that meet at right angles are perpendicular lines.
Therefore, option C correctly describes parallel lines.
Correct Answer: C. They remain the same distance apart and never meet.
Question 2: Finding an Angle on a Straight Line
Two adjacent angles form a straight line. One angle measures $$74^\circ$$. What is the measure of the other angle?
A. $$96^\circ$$
B. $$106^\circ$$
C. $$116^\circ$$
D. $$126^\circ$$
Answer: B. $$106^\circ$$
Concept: Angles on a straight line.
Formula:
$$\text{Angle 1}+\text{Angle 2}=180^\circ$$
Solution:
Let the unknown angle be $$x$$.
$$74^\circ+x=180^\circ$$
Subtract $$74^\circ$$ from both sides:
$$x=180^\circ-74^\circ$$
$$x=106^\circ$$
Therefore, the other angle measures $$106^\circ$$.
Correct Answer: B. $$106^\circ$$
Question 3: Perpendicular Lines
Two perpendicular lines intersect at point O. What is the measure of each angle formed at the intersection?
A. $$45^\circ$$
B. $$60^\circ$$
C. $$90^\circ$$
D. $$180^\circ$$
Answer: C. $$90^\circ$$
Concept: Perpendicular lines.
Explanation:
Perpendicular lines intersect at right angles. A right angle measures:
$$90^\circ$$
Two perpendicular straight lines form four right angles at their intersection.
Therefore, each angle measures $$90^\circ$$.
Correct Answer: C. $$90^\circ$$
Question 4: Vertically Opposite Angles
Two straight lines intersect. One angle measures $$127^\circ$$. What is the measure of the angle directly opposite it?
A. $$53^\circ$$
B. $$63^\circ$$
C. $$127^\circ$$
D. $$180^\circ$$
Answer: C. $$127^\circ$$
Concept: Vertically opposite angles.
Explanation:
When two straight lines intersect, vertically opposite angles are equal.
Therefore, the angle directly opposite the given angle also measures:
$$127^\circ$$
The angles adjacent to it would each measure:
$$180^\circ-127^\circ=53^\circ$$
However, the question asks for the angle directly opposite the given angle.
Correct Answer: C. $$127^\circ$$
Question 5: Finding an Unknown Angle Using Algebra
Two vertically opposite angles measure $$(3x+15)^\circ$$ and $$(5x-25)^\circ$$. Find the value of $$x$$.
A. $$15$$
B. $$20$$
C. $$25$$
D. $$30$$
Answer: B. $$20$$
Concept: Vertically opposite angles and algebra.
Explanation:
Vertically opposite angles are equal.
Therefore:
$$3x+15=5x-25$$
Subtract $$3x$$ from both sides:
$$15=2x-25$$
Add $$25$$ to both sides:
$$40=2x$$
Divide both sides by $$2$$:
$$x=20$$
Check the angle measurements:
$$3(20)+15=75^\circ$$
$$5(20)-25=75^\circ$$
Both expressions give the same angle.
Correct Answer: B. $$20$$
Important Formulas & Concepts
Parallel Lines
Parallel straight lines in the same plane never intersect.
Intersecting Lines
Two lines are intersecting lines if they meet at a common point.
Perpendicular Lines
Perpendicular lines intersect at right angles.
$$\text{Angle between perpendicular lines}=90^\circ$$
Angles on a Straight Line
Angles forming a straight angle add up to:
$$180^\circ$$
Vertically Opposite Angles
Vertically opposite angles are equal.
$$\angle A=\angle C$$
Related Practice Questions
Try solving these questions independently.
- Find the angle that forms a straight angle with $$119^\circ$$.
- Two vertically opposite angles are represented by $$(4x+8)^\circ$$ and $$(6x-32)^\circ$$. Find $$x$$.
- What is the measure of each angle formed by two perpendicular straight lines?
- Explain why two parallel lines do not intersect.
- If one angle formed by two intersecting lines is $$108^\circ$$, find its vertically opposite angle.
Mini Quiz Challenge
Question 1
Which pair of lines intersects at right angles?
A. Parallel lines
B. Perpendicular lines
C. Curved lines
D. Non-intersecting lines
Answer: B. Perpendicular lines
Question 2
What is the supplement of $$83^\circ$$?
A. $$87^\circ$$
B. $$97^\circ$$
C. $$107^\circ$$
D. $$117^\circ$$
Answer: B. $$97^\circ$$
Question 3
Two vertically opposite angles are $$(2x+20)^\circ$$ and $$(4x-30)^\circ$$. Find $$x$$.
A. $$15$$
B. $$20$$
C. $$25$$
D. $$30$$
Answer: C. $$25$$
Exam Tips
- Remember that parallel lines do not intersect.
- Perpendicular lines form right angles of $$90^\circ$$.
- Angles on a straight line add up to $$180^\circ$$.
- Vertically opposite angles are equal.
- Form an equation when angle measurements contain variables.
- Verify algebraic answers by substituting them into the original expressions.
Quick Revision Notes
- Parallel lines remain the same distance apart.
- Intersecting lines meet at a point.
- Perpendicular lines form right angles.
- A straight angle measures $$180^\circ$$.
- Vertically opposite angles are equal.
- Algebra can be used to calculate unknown angles.
Common Mistakes Students Make
- Confusing parallel lines with perpendicular lines.
- Assuming all intersecting lines meet at right angles.
- Treating adjacent angles as vertically opposite angles.
- Forgetting to subtract a known angle from $$180^\circ$$.
- Making arithmetic mistakes while solving equations.
Key Takeaways
Parallel lines, intersecting lines, and perpendicular lines have different geometric properties. Understanding these differences helps students identify line relationships and calculate unknown angles. The properties of straight angles and vertically opposite angles also provide reliable methods for solving geometry problems.
FAQs
1. What are parallel lines?
Parallel lines are straight lines in the same plane that remain the same distance apart and never intersect.
2. What are intersecting lines?
Intersecting lines meet at a common point.
3. What are perpendicular lines?
Perpendicular lines intersect at right angles measuring $$90^\circ$$.
4. What is the sum of angles on a straight line?
The sum is $$180^\circ$$.
5. Are vertically opposite angles equal?
Yes. Vertically opposite angles formed by two intersecting straight lines are equal.
Conclusion
This practice set covers parallel lines, intersecting lines, perpendicular lines, straight angles, and vertically opposite angles. Students should practise the questions and review the explanations to improve their understanding of Class 7 geometry.
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