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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 (EX 3.2)

Free PDF download of NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.2 and all chapter exercises at one place prepared by expert teacher as per NCERT (CBSE) books guidelines. Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise 3.2 Questions with Solutions to help you to revise complete Syllabus and Score More marks. Register and get all exercise solutions in your emails. Vedantu is a platform that provides free NCERT Solution and other study materials for students. Science Students who are looking for NCERT Solutions for Class 8 Science will also find the Solutions curated by our Master Teachers really Helpful.


Class:

NCERT Solutions for Class 8

Subject:

Class 8 Maths

Chapter Name:

Chapter 3 - Understanding Quadrilaterals

Exercise:

Exercise - 3.2

Content-Type:

Text, Videos, Images and PDF Format

Academic Year:

2023-24

Medium:

English and Hindi

Available Materials:

  • Chapter Wise

  • Exercise Wise

Other Materials

  • Important Questions

  • Revision Notes

Access NCERT Solutions for Maths Chapter 3 – Understanding Quadrilaterals

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 $\text{12}{{\text{0}}^{\text{o}}}$.

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

Opting for the NCERT solutions for Ex 3.2 Class 8 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 3.2 Class 8 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 8 students who are thorough with all the concepts from the Maths textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 8 Maths Chapter 3 Exercise 3.2 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.

Besides these NCERT solutions for Class 8 Maths Chapter 3 Exercise 3.2, there are plenty of exercises in this chapter which contain innumerable questions as well. All these questions are solved/answered by our in-house subject experts as mentioned earlier. Hence all of these are bound to be of superior quality and anyone can refer to these during the time of exam preparation. In order to score the best possible marks in the class, it is really important to understand all the concepts of the textbooks and solve the problems from the exercises given next to it. 

Do not delay any more. Download the NCERT solutions for Class 8 Maths Chapter 3 Exercise 3.2 from Vedantu website now for better exam preparation. If you have the Vedantu app in your phone, you can download the same through the app as well. The best part of these solutions is these can be accessed both online and offline as well.

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.