class 8 maths chapter 3 exercise 3.3 solutions explained in detail with step-by-step answers to help students understand and score better in examinations.
1. In a parallelogram ABCD, if angle A is 60 degrees, what is the measure of angle C?
Since opposite angles in a parallelogram are equal, angle C is also 60 degrees.
2. A quadrilateral has three angles measuring 80 degrees each. What is the measure of the fourth angle?
The sum of angles in a quadrilateral is 360 degrees. So, the fourth angle is 360° - (80° + 80° + 80°) = 120°.
3. In parallelogram PQRS, if angle P is 110 degrees, what is the measure of angle Q?
Adjacent angles in a parallelogram are supplementary. Therefore, angle Q = 180° - 110° = 70°.
4. Can a quadrilateral with sides 5 cm, 5 cm, 8 cm, and 8 cm be a parallelogram?
Yes, if both pairs of opposite sides are equal, the quadrilateral is a parallelogram.
5. In a parallelogram, one angle is twice its adjacent angle. What are the measures of these angles?
Let the smaller angle be x. Then the larger angle is 2x. Since adjacent angles are supplementary: x + 2x = 180°; 3x = 180°; x = 60°. So, the angles are 60° and 120°.
6. If the diagonals of a parallelogram are equal, what special type of parallelogram is it?
It's a rectangle.
7. In parallelogram ABCD, if angle A is 75 degrees, what is angle B?
Angle B = 180° - 75° = 105°.
8. A parallelogram has sides 6 cm and 10 cm. What is its perimeter?
Perimeter = 2 × (6 cm + 10 cm) = 32 cm.
9. In a parallelogram, if one angle is 90 degrees, what shape is it?
It's a rectangle.
10. Can a parallelogram have all angles equal? If yes, what is it called?
Yes, it's called a rectangle.
11. In parallelogram ABCD, if diagonal AC bisects angle A, what type of parallelogram is ABCD?
It's a rhombus.
12. If the diagonals of a parallelogram bisect each other at right angles, what is the shape?
It's a rhombus.
13. In a parallelogram, if one angle is 70 degrees, what are the measures of the other angles?
The angles are 70°, 110°, 70°, and 110°.
14. Can a parallelogram have exactly one right angle?
No, if one angle is 90°, all angles are 90°, making it a rectangle.
15. In parallelogram ABCD, if AB = 8 cm and BC = 6 cm, what is the perimeter?
Perimeter = 2 × (8 cm + 6 cm) = 28 cm.
16. If the diagonals of a parallelogram are equal and perpendicular, what is the shape?
It's a square.
17. In a parallelogram, if one angle is 120 degrees, what is the measure of its adjacent angle?
Adjacent angle = 180° - 120° = 60°.
18. Can a parallelogram have sides of different lengths?
No, opposite sides of a parallelogram are always equal.
19. In parallelogram ABCD, if angle A is 85 degrees, what is angle D?
Angle D = 85° (opposite angles are equal).
20. If a parallelogram has all sides equal and angles of 90 degrees, what is it called?
It's a square.
21. In a parallelogram, if the diagonals are equal, what can we conclude about its angles?
All angles are 90 degrees; it's a rectangle.
22. Can a parallelogram have diagonals that are not equal?
Yes, in general, parallelograms have diagonals of different lengths unless it's a rectangle or square.
23. In parallelogram ABCD, if AB = 12 cm and AD = 9 cm, what is the perimeter?
Perimeter = 2 × (12 cm + 9 cm) = 42 cm.
24. If the diagonals of a parallelogram bisect each other but are not equal, what is the shape?
It's a general parallelogram.
25. In a parallelogram, if one angle is 88 degrees, what are the measures of the other angles?
The angles are 88°, 92°, 88°, and 92°.
26. Can a parallelogram have all sides equal but angles that are not 90 degrees?
Yes, it's called a rhombus.
27. In parallelogram ABCD, if angle A is 95 degrees, what is angle B?
Angle B = 180° - 95° = 85°.
28. If a parallelogram has one pair of sides equal and one pair not equal, is it still a parallelogram?
No, both pairs of opposite sides must be equal.
29. In a parallelogram, if the diagonals are equal, what type of angles does it have?
All angles are 90 degrees; it's a rectangle.
30. Can a parallelogram have diagonals that do not bisect each other?
No, in all parallelograms, diagonals bisect each other.
31. In parallelogram ABCD, if AB = 7 cm and AD = 24 cm, what is the perimeter?
Perimeter = 2 × (7 cm + 24 cm) = 62 cm.
32. If the diagonals of a parallelogram are perpendicular but not equal, what is the shape?
It's a rhombus.
33. In a parallelogram, if one angle is 110 degrees, what are the measures of the other angles?
The angles are 110°, 70°, 110°, and 70°.
34. Can a parallelogram have all angles equal but sides of different lengths?
No, if all angles are equal (90°), opposite sides must also be equal; it's a rectangle.
35. In parallelogram ABCD, if angle A is 78 degrees, what is angle D?
Angle D = 78° (opposite angles are equal).
36. If a parallelogram has all sides and angles equal, what is it called?
It's a square.
37. In a parallelogram, if the diagonals are not equal, what can we conclude about its angles?
The angles are not necessarily 90°; it's a general parallelogram or rhombus.
**38. Can a parallelogram have sides of lengths 5 cm, 10 cm, 5 cm, and
Top Recommended Indian Books for Class 8 Maths Chapter 3 Exercise 3.3 Solutions
NCERT Mathematics Textbook for Class 8
Author: NCERT Faculty
Publisher: NCERT
Focuses on the basics of understanding quadrilaterals with standard theory and examples followed by Exercise 3.3. Contains conceptual and application-based questions.
Mathematics for Class 8 by R.D. Sharma
Author: Dr. R.D. Sharma
Publisher: Dhanpat Rai Publications
Offers detailed explanations, multiple solved problems, and extra practice sets for every exercise including 3.3, ideal for mastering geometry topics like parallelograms and types of quadrilaterals.
All-in-One Mathematics Class 8
Author: Arihant Experts
Publisher: Arihant Publications
Covers each NCERT exercise with step-by-step solutions and practice questions. Exercise 3.3 includes MCQs, HOTS, and skill-based questions.
Together With Mathematics Class 8
Author: Rachna Sagar Experts
Publisher: Rachna Sagar Pvt Ltd
Provides explanations aligned with NCERT and CBSE guidelines. Exercise 3.3 includes visual explanations and sample worksheets.
Understanding Mathematics Class 8
Author: M.L. Aggarwal
Publisher: Avichal Publishing Company
Contains deep theory and a logical structure of solutions. The exercise covers real-life application-based problems related to quadrilaterals.
CBSE Chapterwise Mathematics Class 8
Author: Oswal Experts
Publisher: Oswal Publishers
Divides chapters into smaller segments with focused questions. Exercise 3.3 solutions are followed by test papers and model questions.
Mathematics Today Class 8
Author: S.K. Gupta & Anubhuti Gangal
Publisher: S. Chand Publishing
Integrates examples, NCERT solutions, and modern-day application questions. Exercise 3.3 is supported with multiple diagrams and quick tips.
Exemplar Problems – Mathematics Class 8
Author: NCERT
Publisher: NCERT
Meant for deeper conceptual learning with tricky, advanced-level problems. Exercise 3.3 includes extra thought-provoking questions.
Xam Idea Mathematics Class 8
Author: Editorial Board
Publisher: VK Global Publications
Includes basic-to-advanced level questions, case-based problems, and summaries for revision. Helpful for Exercise 3.3 step-by-step solutions.
Mathematics Success Series Class 8
Author: G. Dorairaj
Publisher: Oxford University Press
Blends theory with practice questions. Exercise 3.3 includes engaging activities and mind maps.
Super Refresher Mathematics Class 8
Author: M.L. Aggarwal
Publisher: Arya Publications
Covers concept-building questions and provides answer keys for self-assessment. Especially useful for mastering quadrilaterals in Exercise 3.3.
Maths Lab Activity Book for Class 8
Author: R.P. Rana
Publisher: Sultan Chand
Focuses on activity-based learning with models and lab work. Exercise 3.3 is linked to hands-on geometry activities.
Practice Book Mathematics Class 8
Author: Bharti Bhawan Editorial Team
Publisher: Bharti Bhawan Publishers
Ideal for additional practice with simple explanations. Questions for Exercise 3.3 are structured in increasing difficulty.
New Learner’s Mathematics Class 8
Author: K.S. Randhawa
Publisher: Evergreen Publications
Offers conceptual explanations followed by extensive exercises. Contains extra questions for 3.3 with diagrams and real-life examples.
Self-Study in Mathematics Class 8
Author: T.R. Jain
Publisher: Lakshmi Publications
Includes short theory notes, solved examples, and model tests for each chapter including Exercise 3.3.
Class 8 Maths Chapter 3 Exercise 3.3 Solutions – An Expert Guide for Students
Understanding quadrilaterals is a foundational skill in geometry, and Class 8 Maths Chapter 3 delves deep into this topic. Exercise 3.3 focuses primarily on the properties of parallelograms and other related shapes, testing a student’s conceptual grasp in simple yet effective ways.
This exercise introduces learners to practical applications of geometrical rules. Questions are designed to encourage thinking rather than memorization. For instance, students often solve problems that involve identifying angle measures, classifying types of quadrilaterals, and justifying the reasoning behind their answers. These problem-solving tasks develop logical thinking and spatial reasoning.
One important strategy when approaching Exercise 3.3 is visualization. Encouraging students to draw each quadrilateral helps them understand side lengths, angle relationships, and symmetry more clearly. Teachers often recommend working with graph paper or using paper folding to demonstrate how diagonals bisect each other in parallelograms, which is a key part of many questions.
Another effective method is exploring patterns in the angle relationships. For example, the idea that adjacent angles in a parallelogram are supplementary can unlock many answers without any formulas. These small discoveries make the learning process more engaging and build confidence.
For students looking to strengthen their understanding, using a variety of books is helpful. NCERT provides a strong base, but other books offer added perspectives, alternate solution methods, and different styles of questions. Practice books also tend to include higher-order thinking questions and case-based problems which are in line with the latest CBSE trends.
Time management is another skill that students begin to develop through this exercise. By solving similar types of problems with slight variations, learners gradually speed up without compromising accuracy. This is especially beneficial in competitive exams and school assessments.
Parents and teachers can enhance engagement by relating shapes in Exercise 3.3 to real-world objects — windows, tables, or even mobile screens. These connections help learners realize that geometry isn’t confined to the classroom but is present in everyday life.
Overall, this exercise builds the base for higher geometry in future classes. With proper guidance, the right books, and consistent practice, students can master the topic efficiently and with genuine interest.
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