# NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals (EX 3.3) Exercise 3.3

The NCERT books, which are the main textbooks for CBSE students, can help students become adequately prepared for their upcoming ventures. NCERT books are very beneficial in terms of strengthening students’ fundamental knowledge and providing a number of advantages. NCERT books may be used to build a solid understanding of the key ideas of every subject. The NCERT textbooks should be read in their entirety so that students may understand the concepts. Long-term benefits are probable because students who possess the necessary conceptual clarity are better equipped to work through problems swiftly and efficiently. Students are relieved of the burden of memorization because of conceptual comprehension.

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**NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals (EX 3.3) Exercise 3.3 **

These topics aim to enhance classroom instruction while also being crucial for exams. Students might benefit from completing the self-evaluation exercises in the book and understanding the fundamental strategies for dealing with challenging circumstances. Students can refer to the NCERT Solutions For Class 8 Maths Chapter 3 Practice 3.3, for a better understanding of the exercises. Class 8 Maths Chapter 3 Exercise 3.3 Solutions are easily available on the Extramarks’ website. They may study the material even when they are not connected to the internet by downloading the PDF version of the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3, from the Extramarks website or mobile application.

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The NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3, simplifies the understanding of Class 8 Understanding Quadrilaterals. Class 8 is an important time in students’ lives since it acts as a stepping stone after Class 7. Since Extramarks adheres to the structure of the NCERT Mathematics textbook, students who use Extramarks’ NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3 will never be confused by any of the questions. For students’ academic aspirations, eighth grade is a crucial year. The NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3, can be used as a reference when studying Chapter 3. Students having doubts regarding Class 8 Maths Chapter 3.3 can refer to the NCERT solutions available on the Extramarks’ website.

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The NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3, are required for students planning to score higher in their examinations. NCERT books make students’ comprehension crystal clear so that they can answer any questions that may be presented during board examinations or annual examinations. In order to ensure that students have no trouble answering problems, Extramarks focuses on the NCERT books while also providing solutions to a range of other publications. All CBSE requirements are fully and completely met by the NCERT texts. NCERT is the leading management and research organisation in the country.

The Extramarks website and mobile application offer all the resources needed for competitive exam preparation. Extramarks is a resource that students may use to prepare for a range of competitive exams, such as JEE Mains, NEET, JEE Advance, CUET, and others. Every chapter and subject’s solutions are available on Extramarks. For more help with any of the chapters, students may visit the Extramarks website and download various solutions, like the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3, in PDF format.

Students need to become familiar with the NCERT solutions in order to do well on the Class 8 examination. These NCERT problems have been solved by Mathematics experts from Extramarks. The NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3, will help students comprehend and respond to a variety of questions from Chapter 3 titled “Understanding Quadrilaterals.” With the board examination in mind, students should concentrate on Class 8 Mathematics. Each topic requires that students get ready for their examinations. For further information, students might consult the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3. Class 8 students must adhere to the most recent CBSE curriculum in order to comprehend all of the topics and subtopics taught.

**NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals**

The NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3, for Chapter 3 titled “Understanding Quadrilaterals,” are available on the Extramarks website and mobile application for download in PDF format. The Mathematics specialists at Extramarks have created the NCERT Solutions for Chapter 3 Understanding Quadrilaterals with an examination perspective in mind. These answers outline the precise approach to problem resolution. Students will be able to dispel all of their questions about Understanding Quadrilaterals by comprehending the principles employed in the NCERT Solutions for Class 8 available on the Extramarks’ website.

A Polygon is a straightforward closed curve formed entirely of straight lines, according to the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3. As a result, a Polygon with four sides, four angles, and four vertices is said to be a Quadrilateral. Before moving on to learning Quadrilaterals, this chapter begins by exposing youngsters to several very crucial ideas. The categorization of Polygons based on sides, the study of Diagonals, Concave, Convex, Regular, and Irregular Polygons, as well as the Angle Sum Property, are some of the subjects covered in this course. Every concept has been explained clearly in the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3.

The key ideas presented in this chapter include the following: 3.1 Introduction 3.2 Polygons 3.2.1 Classification of Polygons 3.2.2 Diagonals 3.2.3 Convex and Concave Polygons 3.2.4 Regular and Irregular Polygons 3.2.5 Angle Sum Property 3.3 Sum of the Measures of the Exterior Angles of a Polygon 3.4 Kinds of Quadrilaterals 3.4.1 Trapezium 3.4.2 Kite 3.4.3 Parallelogram 3.4.4 Elements of a Parallelogram 3.4.5 Angles of Parallelogram 3.4.6 Diagonals of a parallelogram 3.5 Some special Parallelograms 3.5.1 Rhombus 3.5.2 A Rectangle 3.5.3 A Square.

**What is a Quadrilateral?**

A Quadrilateral is a flat shape with four edges and four corners, also known as vertices. The Quadrilateral has angles at each of its four vertices, or corners. The angles at the vertices of a Quadrilateral ABCD are ∠A, ∠B, ∠C, and ∠D. A quadrilateral has the following sides: AB, BC, CD, and DA. The diagonals are obtained by joining the opposing vertices of the Quadrilateral. The diagonals of the Quadrilateral ABCD are shown in the figure below as AC and BD. All such definitions and questions are solved in the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3.

Based on the measurements of the angles and side lengths, Quadrilateral kinds are identified. All of these quadrilateral designs have four sides because the term “quad” implies “four,” and their combined angles total 360 degrees. These are the several kinds of Quadrilaterals:

- Trapezium
- Parallelogram
- Squares
- Rectangle
- Rhombus
- Kite

Another approach to different kinds of Quadrilaterals is as follows:

- Convex Quadrilaterals: A figure that entirely encloses both of a Quadrilateral’s diagonals.
- Concave Quadrilaterals: One or more of the diagonals extends partially or completely outside of the picture.
- Quadrilaterals that cross: A Quadrilateral in which the two non-adjacent sides do not intersect is not a simple Quadrilateral. Self-intersecting or crossed Quadrilaterals are the names for these Quadrilaterals.

All the topics and subtopics are discussed in the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3. To know more about the Chapter students should access the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3.

**NCERT Class 8 Maths Chapter 3 Simplified – with Extramarks**

The Extramarks website offers students a simple way to acquire the PDF of the NCERT Solutions for Class 8 Maths Chapter 3: Understanding Quadrilaterals. In accordance with NCERT criteria, Extramarks’ subject-matter specialists compile the solutions available on the Extramarks’ website. Students will have a thorough understanding of the subject while responding to the exercise questions. In order for students to understand, Extramarks makes an effort to keep all the responses simple and engaging. They can also download the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3, in addition to the same. It will assist students in understanding the curriculum and achieving high exam scores. Extramarks also offers NCERT solutions for all levels and courses. The NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3, give students a wide range of understanding.

NCERT Solutions for Class 8 Maths Chapter 3 has exercises that are Exercise 3.1 with 7 Questions having 1 Long Answer Question and 6 Short Answer Questions. Exercise 3.2 with 6 Questions having 6 Short Answer Questions. Further Exercise 3.3 with 12 Questions 6 Long Answer Questions, 6 Short Answer Questions, and lastly, Exercise 3.4 with 6 Questions 1 Long Answer Question, and 5 Short Answer Questions. All these solutions are available on Extramarks students can learn easily from NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3.

**NCERT Solutions for Class 8**

Students can access a variety of study resources, like NCERT Solutions for Class 8. All course materials are accessible on the Extramarks website and mobile application. It is advised that students use the Extramarks website to find answers to any significant queries they may have concerning the chapter. Students can also access the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3. They may get notes, important questions, and sample questions along with NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3. With the NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.3, students can access old questions and get assistance with their solutions.

All the other chapters’ NCERT solutions for Class 8 are also available on Extramarks’ website and mobile application.

Chapter 1 Rational Numbers

Chapter 2 Linear Equation

Chapter 3 Understanding Quadrilaterals

Chapter 4 Applied Practical Geometry

Chapter 5 About Data Handling

Chapter 6 Square Square Roots

Chapter 7 Cube And Cube Roots

Chapter 8 Comparing Quantities

Chapter 9 Algebraic Expressions And Identities

Chapter 10 Visualizing Solid Shapes

Chapter 11 Mensuration

Chapter 12 Exponents And Powers

Chapter 13 Direct Inverse Proportions

Chapter 14 Factorisation

Chapter 15 Introduction To Graphs

Chapter 16 Playing With Number

**Q.1 **Given a parallelogram ABCD. Complete each statement along with the definition or property used.

1. AD = ……

2. ∠ DCB = ……

3. OC = ……

*4. m *∠DAB + *m *∠CDA = …..

**Ans**

1. AD = BC

(Opposite sides are of equal length in a parallelogram.)

2. ∠ DCB = ∠ DAB

(Opposite angles are equal in measure.)

3. OC = OA

(In a parallelogram, diagonals bisect each other)

*4. m *∠DAB + *m *∠CDA = 180°

(In a parallelogram, adjacent angles are supplementary to each other.)

**Q.2 **Consider the following parallelograms. Find the values of the unknowns *x*, *y*, *z*.

**Ans**

(i)

$\begin{array}{l}\mathrm{x}+\text{1}00\mathrm{\xb0}=\text{18}0\mathrm{\xb0}\left(\begin{array}{l}\text{Adjacent}\mathrm{}\text{angles of a parallelogram}\\ \text{are supplementary}\end{array}\right)\\ \Rightarrow \mathrm{x}=\text{8}0\mathrm{\xb0}\\ \\ \text{Since opposite angles of a parallelogram are equal}\\ \therefore \angle \mathrm{A}=\angle \mathrm{C}\\ \Rightarrow \mathrm{z}=\mathrm{x}=\text{8}0\mathrm{\xba}\\ \\ \mathrm{Also},\angle \mathrm{B}=\angle \mathrm{D}\\ \mathrm{Hence},\mathrm{y}=\text{1}00\mathrm{\xb0}\text{}\\ \\ \therefore \mathrm{x}=\text{8}0\mathrm{\xb0},\mathrm{y}=100\mathrm{\xb0}\text{\hspace{0.17em}}\mathrm{and}\text{}\mathrm{z}=\text{8}0\mathrm{\xb0}\end{array}$

$\begin{array}{l}\mathrm{Since}\text{}\mathrm{adjacent}\text{}\mathrm{angles}\text{}\mathrm{of}\text{}\mathrm{a}\text{}\mathrm{parallelogram}\text{}\mathrm{are}\\ \mathrm{supplementary},\text{}\mathrm{therefore},\\ 50\mathrm{\xb0}\text{}+\mathrm{y}=\text{}180\mathrm{\xb0}\\ \Rightarrow \mathrm{y}=\text{}130\mathrm{\xb0}\\ \mathrm{Also},\text{opposite angles of a parallelogram are equal}\\ \therefore \mathrm{x}=\mathrm{y}=130\mathrm{\xb0}\\ \\ \text{Now,\u2019z\u2019 and \u2018x\u2019 are the corresponding angles.}\\ \therefore \mathrm{z}=\mathrm{x}=130\mathrm{\xb0}\\ \\ \therefore \mathrm{x}=130\mathrm{\xb0},\mathrm{y}=130\mathrm{\xb0}\text{\hspace{0.17em}}\mathrm{and}\text{}\mathrm{z}=\text{13}0\mathrm{\xb0}\end{array}$

(iii)

\begin{array}{l}\end{array} $\begin{array}{l}\mathrm{x}=\text{9}0\mathrm{\xb0}\text{}\left(\text{Vertically opposite angles}\right)\\ \\ \mathrm{Also},\\ \mathrm{x}+\mathrm{y}+\text{3}0\mathrm{\xb0}=\text{18}0\mathrm{\xb0}\text{}\left(\text{By angle sum property of triangles}\right)\\ \Rightarrow \text{12}0\mathrm{\xb0}+\mathrm{y}=\text{18}0\mathrm{\xb0}\\ \Rightarrow \mathrm{y}=\text{6}0\mathrm{\xb0}\\ \\ \mathrm{Now},\mathrm{z}=\mathrm{y}=\text{6}0\mathrm{\xb0}\text{}\left(\text{Alternate interior angles}\right)\\ \\ \therefore \mathrm{x}=90\mathrm{\xb0},\mathrm{y}=60\mathrm{\xb0}\text{\hspace{0.17em}}\mathrm{and}\text{}\mathrm{z}=60\mathrm{\xb0}\end{array}$

(iv)

$\begin{array}{l}\text{In the given figure},\\ \mathrm{z}=\text{8}0\mathrm{\xb0}\text{}\left(\text{Corresponding angles}\right)\\ \\ \mathrm{y}=\text{8}0\mathrm{\xb0}\left(\text{Opposite angles are equal in a parallelogram}\right)\\ \mathrm{Also},\\ \mathrm{x}+\mathrm{y}=\text{18}0\mathrm{\xb0}\text{}\left(\text{Adjacent angles are supplementary}\right)\\ \Rightarrow \mathrm{x}=\text{18}0\mathrm{\xb0}-\text{8}0\mathrm{\xb0}\\ \text{}=\text{1}00\mathrm{\xb0}\\ \\ \therefore \mathrm{x}=100\mathrm{\xb0},\mathrm{y}=80\mathrm{\xb0}\text{\hspace{0.17em}}\mathrm{and}\text{}\mathrm{z}=80\mathrm{\xb0}\end{array}$

(v)

\begin{array}{l}\end{array}

$\begin{array}{l}\mathrm{y}=\text{112}\mathrm{\xb0}\text{}\left(\text{Opposite angles are equal}\right)\\ \\ \mathrm{In}\text{}\mathrm{a}\text{}\mathrm{triangle},\\ \mathrm{x}+\text{}\mathrm{y}+\text{4}0\mathrm{\xb0}=\text{18}0\mathrm{\xb0}\text{}\left(\text{By angle sum property}\right)\\ \Rightarrow \mathrm{x}+\text{112}\mathrm{\xb0}+\text{4}0\mathrm{\xb0}=\text{18}0\mathrm{\xb0}\\ \Rightarrow \mathrm{x}+\text{152}\mathrm{\xb0}\text{}=\text{18}0\mathrm{\xb0}\\ \Rightarrow \mathrm{x}=\text{28}\mathrm{\xb0}\\ \\ \mathrm{Also},\\ \mathrm{z}=\mathrm{x}=\text{28}\mathrm{\xb0}\text{}\left(\text{Alternate interior angles}\right)\\ \\ \therefore \mathrm{x}=\text{28}\mathrm{\xb0},\mathrm{y}=\text{112}\mathrm{\xb0}\text{\hspace{0.17em}}\mathrm{and}\text{\hspace{0.17em}}\mathrm{z}=\text{28}\mathrm{\xb0}\end{array}$

**Q.3 **Can a quadrilateral ABCD be a parallelogram if

(i) ∠D + ∠B = 180°?

(ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?

(iii) ∠A = 70° and ∠C = 65°?

**Ans**

A parallelogram has opposite sides equal and parallel. The opposite angles are also equal. The adjacent angles are supplementary.

- So, if ∠D + ∠B = 180°, a quadrilateral ABCD may or may not be a parallelogram as all the other conditions of the parallelogram should also be fulfilled by a quadrilateral ABCD.
- In a parallelogram the opposite sides should be of equal length. Here, AB is equal to CD but AD is not equal to BC. Hence, ABCD is not a parallelogram.
- In a parallelogram the opposite angles are of equal length. Here, ∠A is not equal to ∠C. Hence, ABCD is not a parallelogram.

**Q.4 **Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.

**Ans**

Here, ABCD is a quadrilateral that is not a parallelogram but ∠B=∠D.

**Q.5 **The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of each of the angles of the parallelogram.

**Ans**

$\begin{array}{l}\text{The two angles are in the ratio 3 : 2.}\\ \text{Let}\angle \text{A = 3x and}\angle \text{B = 2x}\\ \text{We know that , the adjacent angles are supplementary in a parallelogram.}\end{array}$ $\begin{array}{l}\therefore \angle \mathrm{A}\text{}+\angle \mathrm{B}\text{}=\text{}180\mathrm{\xb0}\\ \Rightarrow 3\mathrm{x}+\text{}2\mathrm{x}=\text{}180\mathrm{\xb0}\\ \Rightarrow 5\mathrm{x}=\text{}180\mathrm{\xb0}\\ \Rightarrow \mathrm{x}=\frac{180\mathrm{\xb0}}{5}=36\mathrm{\xb0}\\ \mathrm{Hence},\\ \angle \mathrm{A}=3\mathrm{x}=3\times 36\mathrm{\xb0}=108\mathrm{\xb0}\text{}\\ \angle \mathrm{B}=2\mathrm{x}=2\times 36\mathrm{\xb0}=72\mathrm{\xb0}\\ \\ \mathrm{Since},\text{opposite angles of a paralle}\mathrm{log}\text{ra}\mathrm{m}\text{}\mathrm{are}\\ \mathrm{equal},\mathrm{therefore},\\ \text{}\angle \text{A=}\angle \text{C and}\angle \text{B=}\angle \text{D}\\ \therefore \angle \mathrm{A}=\angle \mathrm{C}\text{}=\text{}108\mathrm{\xb0}\text{\hspace{0.17em}}\mathrm{and}\text{}\angle \mathrm{B}=\angle \mathrm{D}=72\mathrm{\xb0}\\ \text{}\end{array}$

Thus, the measures of the angles of the parallelogram are 108°, 72°, 108°, and 72°.

**Q.6 **Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.

**Ans**

In a parallelogram the adjacent angles are supplementary

$\begin{array}{l}\therefore \angle \text{A}+\angle \text{B}=\text{18}0\mathrm{\xb0}\\ \text{Since}\angle \text{A}=\angle \text{B},\\ \Rightarrow \text{2}\angle \text{A}=\text{18}0\mathrm{\xb0}\text{}\\ \Rightarrow \angle \text{A}=\text{9}0\mathrm{\xb0}\\ \Rightarrow \angle \text{B}=\text{9}0\mathrm{\xb0}\\ \\ \mathrm{Now},\angle \text{C}=\angle \text{A}\left(\text{Opposite angles}\right)\\ \Rightarrow \angle \text{C}=\text{9}0\mathrm{\xb0}\\ \angle \text{D}=\angle \text{B}\left(\text{Opposite angles}\right)\\ \Rightarrow \angle \text{D}=\text{9}0\mathrm{\xb0}\\ \text{}\\ \text{Hence},\text{all the angles of the parallelogram are 9}0\mathrm{\xba}.\end{array}$

**Q.7** The adjacent figure HOPE is a parallelogram. Find the angle measures *x*, *y *and *z*. State the properties you use to find them.

**Ans**

$\begin{array}{l}\text{7}0\mathrm{\xb0}=\mathrm{z}\text{}+\text{4}0\mathrm{\xb0}\text{}\left(\text{Corresponding angles of a parallelogram}\right)\\ \Rightarrow \text{7}0\mathrm{\xb0}-\text{4}0\mathrm{\xb0}=\mathrm{z}\\ \Rightarrow \text{z}=\text{3}0\mathrm{\xb0}\\ \\ \mathrm{Also},\\ \mathrm{y}=\text{4}0\mathrm{\xb0}\text{}\left(\text{Alternate interior angles}\right)\\ \\ \mathrm{Now},\angle \mathrm{E}+\angle \mathrm{H}=180\mathrm{\xb0}\left(\text{Adjacent angles are supplementary}\right)\\ \Rightarrow \mathrm{x}+(\mathrm{z}\text{}+\text{4}0\mathrm{\xba})=\text{18}0\mathrm{\xb0}\text{}\\ \Rightarrow \mathrm{x}+(30\mathrm{\xb0}\text{}+\text{4}0\mathrm{\xba})=\text{18}0\mathrm{\xb0}\text{}\\ \Rightarrow \mathrm{x}+\text{7}0\mathrm{\xb0}=\text{18}0\mathrm{\xb0}\\ \Rightarrow \mathrm{x}=\text{11}0\mathrm{\xb0}\\ \\ \therefore \mathrm{x}=\text{11}0\mathrm{\xb0},\mathrm{y}=40\mathrm{\xb0}\text{}\mathrm{and}\text{\hspace{0.17em}}\mathrm{z}=30\mathrm{\xb0}\end{array}$

**Q.8 **The following figures GUNS and RUNS are parallelograms . Find *x *and *y*. (Lengths are in cm)

**Ans**

(i) We know that, the lengths of opposite sides of a parallelogram are equal to each other.

Therefore, GU = SN and SG =NU

$\begin{array}{l}\Rightarrow \text{3}\mathrm{y}-\text{1}=\text{26}\\ \Rightarrow \text{3}\mathrm{y}=\text{27}\\ \Rightarrow \mathrm{y}=\text{9}\\ \\ \text{Also, SG}=\text{NU}\\ \Rightarrow \text{3}\mathrm{x}=\text{18}\\ \Rightarrow \mathrm{x}=\text{6}\end{array}$

Hence, the measures of *x* and *y* are 6 cm and 9 cm.

(ii) We know that the diagonals of a parallelogram bisect each other.

$\begin{array}{l}\mathrm{y}+\text{7}=\text{2}0\text{}\mathrm{and}\text{\hspace{0.17em}}\mathrm{x}+\mathrm{y}=\text{16}\\ \\ \mathrm{Now},\mathrm{y}+\text{7}=\text{2}0\text{}\\ \Rightarrow \mathrm{y}=\text{13}\\ \\ \mathrm{Also},\mathrm{x}+\mathrm{y}=\text{16}\\ \Rightarrow \mathrm{x}+\text{13}=\text{16}\\ \Rightarrow \mathrm{x}=\text{3}\end{array}$

Hence, the measures of x and y are 3 cm and 13 cm.

**Q.9 **

In the above figure both RISK and CLUE are parallelograms. Find the value of *x*.

**Ans**

$\begin{array}{l}\text{In parallelogram RISK},\\ \angle \text{RKS}+\angle \text{ISK}=\text{18}0\xb0\begin{array}{l}\text{}[\text{Adjacent angles of a parallelogram}\\ \text{are supplementary.}]\end{array}\\ \Rightarrow \text{12}0\xb0+\angle \text{ISK}=\text{18}0\xb0\\ \Rightarrow \angle \text{ISK}=\text{6}0\xb0\\ \\ \\ \text{In parallelogram CLUE},\\ \angle \text{ULC}=\angle \text{CEU}=\text{7}0\xb0\left(\begin{array}{l}\text{opposite angles of}\\ \text{a parallelogram are equal}.\end{array}\right)\\ \\ \text{Now, in a triangle,}\\ x+\text{6}0\xb0+\text{7}0\xb0=\text{18}0\xb0\text{}\left(\text{By angle sum property}\right)\\ \Rightarrow x=\text{5}0\xb0\end{array}$

**Q.10 **Explain how this figure is a trapezium. Which of its two sides are parallel?

**Ans**

Here, ∠NML + ∠MLK = 180°

Hence, NM||LK and ML is a transversal.(If a transversal intersects the two given lines such that the sum of the angles on the same side of transversal is 180º, then the given two lines will be parallel to each other.)

Therefore, KLMN is a trapezium as it has one pair of parallel lines.

**Q.11 **

$\mathrm{Find}\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{m}\angle \mathrm{C}\mathrm{in}\mathrm{Fig}.\mathrm{if}\text{\hspace{0.17em}}\overline{\mathrm{AB}}\left|\right|\overline{\mathrm{DC}}.$

**Ans**

$\begin{array}{l}\mathrm{}\text{Given}:\mathrm{AB}\left|\right|\mathrm{BC}\\ \Rightarrow \angle \text{B}+\angle \text{C}=\text{18}0\mathrm{\xb0}\begin{array}{l}[\text{Angles on the same side of transversal}\\ \text{are supplementary}.]\text{}\end{array}\\ \Rightarrow \text{12}0\mathrm{\xb0}+\angle \text{C}=\text{18}0\mathrm{\xb0}\\ \Rightarrow \angle \text{C}=\text{6}0\mathrm{\xb0}\end{array}$

**Q.12 **

$\begin{array}{l}\mathrm{Find}\mathrm{the}\mathrm{measure}\mathrm{of}\angle \mathrm{P}\mathrm{and}\angle \mathrm{S}\mathrm{if}\text{\hspace{0.17em}}\mathrm{SP}\left|\right|\mathrm{RQ}\mathrm{in}\mathrm{Fig}.(\mathrm{If}\mathrm{you}\mathrm{find}\text{\hspace{0.17em}}\\ \mathrm{m}\angle \mathrm{R},\mathrm{is}\mathrm{there}\mathrm{more}\mathrm{than}\mathrm{one}\mathrm{method}\mathrm{to}\mathrm{find}\text{\hspace{0.17em}}\mathrm{m}\angle \mathrm{P}?)\end{array}$

**Ans**

$\begin{array}{l}\mathrm{Given}:\mathrm{SP}\left|\right|\mathrm{RQ}\\ \therefore \angle \text{P}+\angle \text{Q}=\text{18}0\mathrm{\xb0}\text{}\left(\text{Angles on the same side of transversal}\right)\\ \Rightarrow \angle \text{P}+\text{13}0\mathrm{\xb0}=\text{18}0\mathrm{\xb0}\\ \Rightarrow \angle \text{P}=\text{5}0\mathrm{\xb0}\\ \\ \mathrm{Also},\\ \angle \text{R}+\angle \text{S =18}0\mathrm{\xb0}\text{}\left(\text{Angles on the same side of transversal}\right)\\ \Rightarrow \text{9}0\mathrm{\xb0}+\angle \text{R}=\text{18}0\mathrm{\xb0}\\ \Rightarrow \angle \text{S}=\text{9}0\mathrm{\xb0}\\ \end{array}$

$\begin{array}{l}\text{Yes,}\text{there is one more method to find the measure of}\angle \text{P}.\\ \text{We can apply the angle sum property of a quadrilateral}\\ \text{to find the}\mathrm{m}\angle \text{P}.\end{array}$

##### FAQs (Frequently Asked Questions)

## 1. What is the definition of Quadrilaterals according to the NCERT Book of Class 8?

According to NCERT Solutions for Class 8 Maths Chapter 3, a Quadrilateral is a plane figure that has four sides or edges, and also has four corners or vertices. Quadrilaterals will typically be of standard shapes with four sides like rectangle, square, trapezoid, and kite.

## 2. Are the topics included in the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3 prepared in accordance with the NCERT Mathematics book?

In accordance with the NCERT Mathematics book, the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3 have been compiled. After reading from NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3, the professionals constantly make sure that NCERT books remain at the centre of their study material so that students can quickly refer to these solutions when solving questions from the NCERT Mathematics textbook.

## 3. Are the NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3 compiled in accordance with the updated syllabus of Maths Class 8?

Yes, Extramarks keeps track of all updates and new topics added to the syllabus. They leave no stone unturned in order to ensure that students face no difficulties. As a result, NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3 are from the most recent syllabus, as experts always make changes when something new arises.

## 4. Why are NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3 significant?

The NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3 are crucial, without a question. Students do not have to worry about anything when receiving NCERT Solutions For Class 8 Maths Chapter 3 Exercise 3.3 since they come with topic-specific notes and solutions to NCERT questions. They only need to focus on studying intently, and ultimately they will be able to put all of their doubts to rest.