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NCERT Solutions for Class 8 Maths Chapter 3 - Understanding Quadrilaterals Exercise 3.2

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NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.2 - FREE PDF Download

Free PDF download of NCERT Solutions for Maths Chapter 3 Ex 3.2 class 8 and all chapter exercises in one place prepared by an expert teacher as per NCERT (CBSE) book guidelines. Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 class 8 Questions with Solutions focuses on the study of quadrilaterals. Key topics include the classification of quadrilaterals (such as parallelograms, rectangles, rhombuses, and squares), their unique properties, and the angle sum property of quadrilaterals. This exercise aims to build a solid foundation in understanding the characteristics and properties of various quadrilaterals, enhancing students' geometric problem-solving abilities.

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Table of Content
1. NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.2 - FREE PDF Download
2. Glance of NCERT Solutions for Maths Class 8 Exercise 3.2 of Chapter 3 | Vedantu
3. Access PDF for Class 8 Maths NCERT Chapter 3 Understanding Quadrilaterals Exercise 3.2
4. Class 8 Maths Chapter 3: Exercises Breakdown
5. CBSE Class 8 Maths Chapter 3 Other Study Materials
6. Chapter-Specific NCERT Solutions for Class 8 Maths
FAQs


Glance of NCERT Solutions for Maths Class 8 Exercise 3.2 of Chapter 3 | Vedantu

  • Chapter 3 Understanding Quadrilaterals Ex 3.2 class 8 focus on applying the concept of exterior angles in quadrilaterals.

  • Class 8 maths exercise 3.2 solutions address various problems that ask you to find unknown angles or properties of quadrilaterals.

  • Find unknown angles in a quadrilateral given the measures of other angles.

  • Find the angles of a quadrilateral given the ratio of their measures.

  • Find the measure of each of the equal angles in a quadrilateral given the measures of two other angles.

  • The sum of the exterior angles of any polygon is always 360 degrees. This property holds true for quadrilaterals as well.

  • Class 8 exercise 3.2 Maths NCERT Solutions has over all 6 questions, all 6 are short answers.

Access PDF for Class 8 Maths NCERT Chapter 3 Understanding Quadrilaterals Exercise 3.2

Exercise 3.2

1. Find $\text{x}$ in the following figures

Triangle


$\left( \text{a} \right)$

Ans: As we can see in the figure and we also know that the sum of all the exterior angles on any polygon is $ 360^{\circ}$, we got

$ \Rightarrow x + 125^{\circ} + 125^{\circ} = 360^{\circ} $

 $ \Rightarrow x + 250^{\circ} =360^{\circ} $ 

 $ \Rightarrow x = 110^{\circ} $

Therefore, we got $x = 110^{\circ}$

Exterior Angle


$\left( \text{b} \right)$

As we can see in the figure and we also know that the sum of all the exterior angles on any polygon is $360^{\circ}$, we got

$ \Rightarrow x + 60^{\circ} + 90^{\circ} + 70^{\circ} + 90^{\circ} = 360^{\circ}$

$ \Rightarrow x + 310^{\circ} = 360^{\circ}$

$ \Rightarrow x = 50^{\circ}$

Therefore, we got $x = 50^{\circ}$.

2. Find the measure of each exterior angle of a regular polygon of 

$\left( \text{i} \right)\text{9}$ sides 

Ans: Now, we know that the sum of the exterior angles of any polygon is $\text{36}{{\text{0}}^{\text{o}}}$.

So, if the polygon has $\text{9}$ sides, the measure of each angle will be $\text{=}\dfrac{\text{36}{{\text{0}}^{\text{o}}}}{\text{9}}\text{=4}{{\text{0}}^{\text{o}}}$.

Therefore, the measure of each angle will be $\text{4}{{\text{0}}^{\text{o}}}$.


$\left( \text{ii} \right)\text{15}$ sides

Ans: Now, we know that the sum of the exterior angles of any polygon is $\text{36}{{\text{0}}^{\text{o}}}$.

So, if the polygon has $\text{15}$ sides, the measure of each angle will be $\text{=}\dfrac{\text{36}{{\text{0}}^{\text{o}}}}{\text{15}}\text{=2}{{\text{4}}^{\text{o}}}$.

Therefore, the measure of each angle will be $\text{2}{{\text{4}}^{\text{o}}}$.


3. How many sides does a regular polygon have if the measure of an exterior angle is $\text{2}{{\text{4}}^{\text{o}}}$?

Ans: Now, we know that the sum of all the measures of any polygon is $\text{36}{{\text{0}}^{\text{o}}}$.

It is given that each angle is of $\text{2}{{\text{4}}^{\text{o}}}$, so, the number of sides in regular polygon will be $\text{=}\dfrac{\text{36}{{\text{0}}^{\text{o}}}}{\text{2}{{\text{4}}^{\text{o}}}}\text{=15}$. 

Therefore, the regular polygon will have $\text{15}$ sides.

4. How many sides does a regular polygon have if the measure of an interior angle is $\text{16}{{\text{5}}^{\text{o}}}$?

Ans: Now, we have interior angle measuring $\text{16}{{\text{5}}^{\text{o}}}$, so the exterior angle will be of $\text{18}{{\text{0}}^{\text{o}}}\text{-16}{{\text{5}}^{\text{o}}}\text{=1}{{\text{5}}^{\text{o}}}$.

We got that the exterior angle is $\text{1}{{\text{5}}^{\text{o}}}$ thus we know that the sum of all the measures of any polygon is $\text{36}{{\text{0}}^{\text{o}}}$.

It is given that each angle is of $\text{1}{{\text{5}}^{\text{o}}}$, so, the number of sides in regular polygon will be $\text{=}\dfrac{\text{36}{{\text{0}}^{\text{o}}}}{\text{1}{{\text{5}}^{\text{o}}}}\text{=24}$.

Therefore, the regular polygon will have $\text{24}$ sides.


5. $\left( \text{a} \right)$ Is it possible to have a regular polygon with measure of each exterior angles as $\text{2}{{\text{2}}^{\text{o}}}$?

Ans: As we know that the sum of all the exterior angles of any polygon is $\text{36}{{\text{0}}^{\text{o}}}$.

Now, if we have to find that if it’s possible to have a regular polygon with a measure of exterior angle, then it is mandatory that $\text{36}{{\text{0}}^{\text{o}}}$ is a perfect multiple of the given exterior angle.

So, as we can see that $\text{36}{{\text{0}}^{\text{o}}}$ is not a perfect multiple of $\text{2}{{\text{2}}^{\text{o}}}$.

Therefore, it is not possible to have a regular polygon with measure of each exterior angles as $\text{2}{{\text{2}}^{\text{o}}}$.


$\left( b \right)$ Is it possible to have a regular polygon with measure of each interior angles as $\text{2}{{\text{2}}^{\text{o}}}$?

Ans: Now, we have interior angle measuring $\text{2}{{\text{2}}^{\text{o}}}$, so the exterior angle will be of $\text{18}{{\text{0}}^{\text{o}}}\text{-2}{{\text{2}}^{\text{o}}}\text{=15}{{\text{8}}^{\text{o}}}$.

We got that the exterior angle is $\text{15}{{\text{8}}^{\text{o}}}$.

As we know that the sum of all the exterior angles of any polygon is $\text{36}{{\text{0}}^{\text{o}}}$.

Now, if we have to find that if it’s possible to have a regular polygon with measure of exterior angle, then it is mandatory that $\text{36}{{\text{0}}^{\text{o}}}$ is a perfect multiple of the given exterior angle.

So, as we can see that $\text{36}{{\text{0}}^{\text{o}}}$ is not a perfect multiple of $\text{15}{{\text{8}}^{\text{o}}}$.

Therefore, it is not possible to have a regular polygon with measure of each exterior angles as $\text{15}{{\text{8}}^{\text{o}}}$.


6. $\left( \text{a} \right)$ What is the minimum interior angle possible for a regular polygon?

Ans: As we needed to find out the minimum interior angle possible for a regular polygon, we will consider a regular polygon with the lowest sides.

The regular polygon with the lowest sides is an equilateral triangle with $\text{3}$ sides

Now, we know that the sum of all the measures of any polygon is $\text{36}{{\text{0}}^{\text{o}}}$.

So, the maximum exterior angle in equilateral triangle will be $\dfrac{\text{36}{{\text{0}}^{\text{o}}}}{\text{3}}\text{=12}{{\text{0}}^{\text{o}}}$.

We got the maximum exterior angle is $\text{12}{{\text{0}}^{\text{o}}}$.

As we know, the sum of all the interior angles in a triangle is $\text{18}{{\text{0}}^{\text{o}}}$.

So, the minimum interior angle will be $\text{18}{{\text{0}}^{\text{o}}}\text{-12}{{\text{0}}^{\text{o}}}\text{=6}{{\text{0}}^{\text{o}}}$, we get the minimum angle as $\text{6}{{\text{0}}^{\text{o}}}$

Therefore, the minimum interior angle is possible for a regular polygon is $\text{6}{{\text{0}}^{\text{o}}}$.

$\left( \text{b} \right)$ What is the maximum exterior angle possible for a regular polygon?

Ans: Now, we know that the maximum exterior angle of a regular polygon is possible if the interior angle of the same polygon is minimum.

Now, we know that the minimum interior angles possible is $\text{6}{{\text{0}}^{\text{o}}}$,

So, the maximum exterior angle possible is $\text{18}{{\text{0}}^{\text{o}}}\text{-6}{{\text{0}}^{\text{o}}}\text{=12}{{\text{0}}^{\text{o}}}$.

Therefore, the maximum exterior angle is $\text{12}{{\text{0}}^{\text{o}}}$.


Conclusion

Exercise 3.2 focuses on exploring various properties and types of quadrilaterals. The exercise provides a series of problems that help students understand the classification and characteristics of different quadrilaterals, such as parallelograms, rhombuses, rectangles, and squares. This chapter is designed to reinforce students' knowledge of quadrilaterals, helping them to distinguish between different types and understand their properties thoroughly. This exercise is essential for building a strong base in geometry, enabling students to tackle more complex geometrical concepts in future studies.


Class 8 Maths Chapter 3: Exercises Breakdown

Chapter 3 - Understanding Quadrilaterals Exercises in PDF Format

Exercise 3.1

2 Questions & Solutions (1 Long Answer, 1 Short Answer)

Exercise 3.3

12 Questions & Solutions (6 Long Answers, 6 Short Answers)

Exercise 3.4

6 Questions & Solutions (1 Long Answer, 5 Short Answers)


CBSE Class 8 Maths Chapter 3 Other Study Materials

Other than Maths Class 8 Chapter 3 Exercise 3.2  you can also check on the additional study materials provided for Class 8 Maths Chapter 3.



Chapter-Specific NCERT Solutions for Class 8 Maths

The chapter-wise NCERT Solutions for Class 8 Maths are given below. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.


FAQs on NCERT Solutions for Class 8 Maths Chapter 3 - Understanding Quadrilaterals Exercise 3.2

1. Where can I find accurate NCERT Solutions for class 8 Maths Chapter 3 Understanding Quadrilaterals (EX 3.2) Exercise 3.2?

You can find accurate NCERT Solutions for class 8 Maths Chapter 3 Understanding Quadrilaterals (EX 3.2) Exercise 3.2 from the Vedantu website. For all of the Class 8 Maths chapters, NCERT Solutions are available on Vedantu, India's top e-learning portal. These solutions were created explicitly by Vedantu subject experts in accordance with CBSE standards. These answers are clear and entirely truthful. You can obtain these study materials in an accessible PDF version by going to the official Vedantu website or mobile app.

2. What is Understanding Quadrilaterals in NCERT Class 8 Maths?

In class 8 math chapter 3, "Understanding Quadrilaterals," a polygon is defined as a straightforward closed curve constructed of straight lines. One sort of polygon that has four sides, four vertices, four angles, and two diagonals is a quadrilateral. As a result, a polygon with four sides, four angles, and four vertices is said to be a quadrilateral. For all the crucial inquiries, NCERT Solutions, review materials, and other study resources for Class 8 Math, students can consult Vedantu.

3. Why should I use Vedantu's NCERT Solutions for Class 8 Mathematics Exercise 3.2, Understanding Quadrilaterals?

If you have the appropriate study resources, getting all A's in math shouldn't be too challenging. Students should practise their respective exercise questions because learning just the chapters is never enough to master a subject like mathematics. NCERT Solutions have been prepared by experienced professionals at Vedantu following CBSE guidelines. The solutions are precisely and fully stated. Using quick problem-solving techniques will help you finish your exam on time, improve your grades, and get ready for difficult exams. On the Vedantu website and mobile app, all of these solutions are available for free download.

4. What do you mean by regular and irregular polygon class 8?

A regular polygon is one that has equal sides and equal angles. A regular polygon with four equal sides and four equal angles is a square. In contrast to regular polygons, which are polygons with equal sides and equal angles, irregular polygons are polygons with unequal angles and sides.

5. What are the topics in class 8 Maths Chapter 3 Understanding Quadrilaterals covered?

Class 8 maths Chapter 3 Understanding Quadrilaterals covers topics such as polygons, classification of polygons, diagonals, convex and concave polygons, regular and irregular polygons, the angle sum property, the sum of measures of exterior angles of polygons, various types of quadrilaterals, trapeziums, kites, and more.


For NCERT math solutions, crucial inquiries, revision notes, and other study materials, students can consult Vedantu.