Class 7 Maths Chapter 5 – Parallel and Intersecting Lines

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Practise Class 7 Maths Chapter 5 MCQs Set 2 on angles, intersecting lines, supplementary angles, perpendicular lines, and angle calculations with detailed solutions.

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Chapter Information

• Class: 7
• Subject: Mathematics
• Chapter: 5 – Parallel and Intersecting Lines
• Practice Set: 2
• Board: CBSE
• Textbook Reference: NCERT Ganita Prakash
• Question Type: Multiple-Choice Questions (MCQs)

Introduction

Lines and angles help us understand the geometric relationships between different shapes and objects. When two straight lines intersect, they form four angles. The relationships between these angles can be used to calculate unknown measurements and solve geometry problems.

This practice set focuses on angle relationships, supplementary angles, perpendicular lines, and calculations involving angles formed by intersecting lines. All questions are independently written for practice.

What Will You Learn?

After completing this practice set, students will be able to:

• Calculate unknown angles using angle relationships.
• Understand supplementary angles.
• Apply the properties of vertically opposite angles.
• Identify perpendicular lines.
• Solve numerical problems involving intersecting lines.

Why Is This Topic Important?

Understanding angle relationships develops logical reasoning and problem-solving skills. These concepts provide a foundation for studying triangles, polygons, and other geometrical figures.

Exam Relevance

Questions from this topic may involve:

• Finding unknown angles.
• Applying supplementary-angle properties.
• Using vertically opposite angles.
• Identifying perpendicular lines.
• Solving simple geometrical calculations.

MCQs with Detailed Solutions

Question 1: Finding a Supplementary Angle

Two angles are supplementary. If one angle measures $$118^\circ$$, what is the measure of the other angle?

A. $$52^\circ$$

B. $$62^\circ$$

C. $$72^\circ$$

D. $$118^\circ$$

Answer: B. $$62^\circ$$

Concept: Supplementary angles.

Formula:

The sum of two supplementary angles is:

$$\text{Angle 1}+\text{Angle 2}=180^\circ$$

Solution:

Let the unknown angle be $$x$$.

$$118^\circ+x=180^\circ$$

Subtract $$118^\circ$$ from both sides:

$$x=180^\circ-118^\circ$$

$$x=62^\circ$$

Therefore, the other angle measures $$62^\circ$$.

Correct Answer: B. $$62^\circ$$

Question 2: Vertically Opposite Angles

Two straight lines intersect. One angle measures $$x^\circ$$, and the angle directly opposite it measures $$(3x-80)^\circ$$. Find the value of $$x$$.

A. $$30^\circ$$

B. $$35^\circ$$

C. $$40^\circ$$

D. $$45^\circ$$

Answer: C. $$40^\circ$$

Concept: Vertically opposite angles.

Explanation:

Vertically opposite angles are equal.

Therefore:

$$x=3x-80$$

Subtract $$x$$ from both sides:

$$0=2x-80$$

Add $$80$$ to both sides:

$$80=2x$$

Divide both sides by $$2$$:

$$x=\frac{80}{2}$$

$$x=40^\circ$$

The angle measures are both $$40^\circ$$.

Correct Answer: C. $$40^\circ$$

Question 3: Angles Around a Point

Three angles around a point measure $$95^\circ$$, $$125^\circ$$, and $$x^\circ$$. What is the value of $$x$$?

A. $$120^\circ$$

B. $$130^\circ$$

C. $$140^\circ$$

D. $$150^\circ$$

Answer: B. $$140^\circ$$

Concept: Angles around a point.

Formula:

The sum of all angles around a point is:

$$360^\circ$$

Solution:

Given angles:

$$95^\circ,\quad 125^\circ,\quad x^\circ$$

Therefore:

$$95^\circ+125^\circ+x=360^\circ$$

Add the known angles:

$$220^\circ+x=360^\circ$$

Subtract $$220^\circ$$:

$$x=360^\circ-220^\circ$$

$$x=140^\circ$$

Correct Answer: C. $$140^\circ$$

Question 4: Identifying an Acute Angle

Which of the following angles is an acute angle?

A. $$35^\circ$$

B. $$90^\circ$$

C. $$115^\circ$$

D. $$180^\circ$$

Answer: A. $$35^\circ$$

Concept: Classification of angles.

Explanation:

An acute angle measures more than $$0^\circ$$ but less than $$90^\circ$$.

A right angle measures exactly $$90^\circ$$. An obtuse angle measures more than $$90^\circ$$ but less than $$180^\circ$$. A straight angle measures $$180^\circ$$.

Since $$35^\circ$$ is less than $$90^\circ$$, it is an acute angle.

Correct Answer: A. $$35^\circ$$

Question 5: Perpendicular Lines and Angle Measures

Two perpendicular lines intersect at point O. What is the sum of three of the angles formed at O?

A. $$180^\circ$$

B. $$270^\circ$$

C. $$300^\circ$$

D. $$360^\circ$$

Answer: B. $$270^\circ$$

Concept: Perpendicular lines and right angles.

Explanation:

Perpendicular lines form four right angles, each measuring:

$$90^\circ$$

The sum of three of these angles is:

$$90^\circ+90^\circ+90^\circ=270^\circ$$

Therefore, the required sum is $$270^\circ$$.

Correct Answer: B. $$270^\circ$$

Important Formulas & Concepts

1. Supplementary Angles

Two angles are supplementary when their sum is $$180^\circ$$.

$$\angle A+\angle B=180^\circ$$

2. Vertically Opposite Angles

Vertically opposite angles formed by two intersecting straight lines are equal.

$$\angle A=\angle C$$

3. Angles Around a Point

The sum of all angles around a point is $$360^\circ$$.

$$\angle 1+\angle 2+\angle 3+\cdots=360^\circ$$

4. Acute Angles

An acute angle is greater than $$0^\circ$$ and less than $$90^\circ$$.

$$0^\circ<\theta<90^\circ$$

5. Perpendicular Lines

Perpendicular lines intersect at right angles.

$$90^\circ$$

Related Practice Questions

Try solving these questions independently.

1. Find the supplement of an angle measuring $$137^\circ$$.
2. Two vertically opposite angles are represented by $$2x+10$$ and $$5x-50$$ degrees. Find $$x$$.
3. Three angles around a point are $$80^\circ$$, $$145^\circ$$, and $$x^\circ$$. Find $$x$$.
4. Is an angle measuring $$89^\circ$$ acute or obtuse?
5. What is the sum of four right angles?

Mini Quiz Challenge

Question 1

What is the supplement of $$76^\circ$$?

A. $$104^\circ$$

B. $$114^\circ$$

C. $$94^\circ$$

D. $$76^\circ$$

Answer: A. $$104^\circ$$

Question 2

Which statement is true for vertically opposite angles?

A. They always add up to $$90^\circ$$.

B. They are always equal.

C. They are always acute.

D. They are always supplementary.

Answer: B. They are always equal.

Question 3

What is the sum of angles around a point?

A. $$90^\circ$$

B. $$180^\circ$$

C. $$270^\circ$$

D. $$360^\circ$$

Answer: D. $$360^\circ$$

Exam Tips

• Remember that supplementary angles add up to $$180^\circ$$.
• Vertically opposite angles are equal.
• The sum of angles around a point is $$360^\circ$$.
• Check whether an angle is acute, right, obtuse, or straight.
• Show each step when solving for an unknown angle.
• Verify calculations before selecting the final option.

Quick Revision Notes

• Supplementary angles have a sum of $$180^\circ$$.
• Vertically opposite angles are equal.
• Angles around a point total $$360^\circ$$.
• Acute angles are smaller than $$90^\circ$$ and greater than $$0^\circ$$.
• Perpendicular lines form four right angles.
• A straight angle measures $$180^\circ$$.

Common Mistakes Students Make

• Confusing supplementary angles with complementary angles.
• Assuming vertically opposite angles are supplementary in every case.
• Forgetting that a complete turn around a point is $$360^\circ$$.
• Classifying an angle of $$90^\circ$$ as acute.
• Making calculation errors when transposing terms in an equation.

Key Takeaways

Angle properties help students solve geometrical problems systematically. Supplementary angles add up to $$180^\circ$$, vertically opposite angles are equal, and the sum of angles around a point is $$360^\circ$$. Understanding these relationships makes it easier to calculate unknown angles and identify different types of angles.

FAQs

1. What are supplementary angles?

Two angles are supplementary if their measures add up to $$180^\circ$$.

2. How are vertically opposite angles related?

Vertically opposite angles are equal when two straight lines intersect.

3. What is the sum of angles around a point?

The sum is $$360^\circ$$.

4. Is an angle of $$89^\circ$$ acute?

Yes. It is greater than $$0^\circ$$ and less than $$90^\circ$$.

5. How many right angles are formed by perpendicular lines?

Two perpendicular straight lines form four right angles, each measuring $$90^\circ$$.

Conclusion

This practice set strengthens understanding of supplementary angles, vertically opposite angles, angles around a point, acute angles, and perpendicular lines. Students should review the formulas and practise solving each question to improve accuracy in geometry.

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