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A geometrical closed shape made by using 4 straight lines and having four connecting points is called a Quadrilateral. The sum of the interior angles in a quadrilateral is always 360 degrees. NCERT Solutions for Class 8 Maths chapter 3, Understanding Quadrilaterals, cover the chapter to help you with the answers and conceptual clarity. It carries around 35% of geometry weightage and includes questions based on concepts of rectangles, squares, rhombuses, parallelograms, trapeziums, etc.
These NCERT Solutions are created by the expert team at Career360, keeping the latest syllabus and pattern of CBSE 2025-26. Practicing questions is important to score good marks in Mathematics. NCERT solutions for Class 8 Maths discussed all questions and answers of all chapters, including Chapter 3, Understanding Quadrilaterals. The subtopics covered in this chapter are polygons, the angle sum property, and properties of different kinds of quadrilaterals. The NCERT solutions for Class 8 Maths chapter 3, Understanding Quadrilaterals, contain the solution to each question in an easy and understandable manner.
Students who wish to access the NCERT solutions for class 8, chapter 3, Understanding Quadrilaterals, can click on the link below to download the entire solution in PDF.
Class 8 Maths Chapter 3 Question Answer: 3.1 Total Questions: 3 Page number: 22 |
Question 1 (a): Given here are some figures.
Classify each of them based on the following.
Answer:
(a) Simple curve: The curve that does not cross itself and has only one curve.
Some simple curves are
Question 1 (b): Given here are some figures.
Classify each of them based on the following.
Answer:
Simple closed curve: A simple curve that is closed by a line segment or curved line.
Some simple closed curves are
Question 1 (c): Given here are some figures.
Classify each of them based on the following.
Answer:
A normally closed curve made up of more than 4 line segments is called a polygon.
Some polygons are shown in Figures
Question 1 (d): Given here are some figures.
Classify each of them based on the following.
Answer:
(d) Convex polygon: Convex polygons are polygons having all interior angles less than
Convex polygon = 2.
Q1 (e) Given here are some figures.
Classify each of them based on the following.
Answer:
(e) Concave polygon: A Concave polygon has one or more interior angles greater than
Concave polygon = 1.
Question 2 (i): What is a regular polygon?
State the name of a regular polygon of 3 sides
Answer:
A regular polygon is a polygon that has equal sides and equal angles.
The name of a regular polygon of 3 sides is an equilateral triangle.
All sides of the equilateral triangle are equal, and the angles are also equal.
Each angle =
Question 2 (ii): What is a regular polygon?
State the name of a regular polygon of 4 sides
Answer:
A regular polygon is a polygon that has equal sides and equal angles.
The name of a regular polygon of 4 sides is a square.
Square has all angles of
Question 2 (iii): What is a regular polygon?
State the name of a regular polygon of 6 sides
Answer:
A regular polygon is a polygon which have equal sides and equal angles.
The name of a regular polygon of 6 sides is a hexagon.
All angles of the hexagon are
Class 8 Maths Chapter 3 Question Answer: 3.2 Total Questions: 6 Page number: 24 |
Question 1 (a): Find
Answer:
The sum of all exterior angles of a polygon is
Question 1 (b): Find
Answer:
The sum of all exterior angles of a polygon is
Question 2 (i): Find the measure of each exterior angle of a regular polygon of 9 sides.
Answer:
A regular polygon of 9 sides has all sides, interior angles, and exterior angles equal.
Sum of exterior angles of a polygon =
Let the interior angle be A.
Sum of exterior angles of 9 sided polygon =
Exterior angles of 9 sided polygon
Hence, the measure of each exterior angle of a regular polygon of 9 sides is
Question 2 (ii): Find the measure of each exterior angle of a regular polygon of 15 sides.
Answer:
A regular polygon of 15 sides has all sides, interior angles, and exterior angles equal.
Sum of exterior angles of a polygon =
Let the interior angle be A.
Sum of exterior angles of 15 sided polygon =
Exterior angles of 15 sided polygon
Hence, the measure of each exterior angle of a regular polygon of 15 sides is
Question 3: How many sides does a regular polygon have if the measure of an exterior angle is 24°?
Answer:
The measure of an exterior angle is 24°
A regular polygon has all exterior angles equal.
Sum of exterior angles of a polygon =
Let the number of sides be X.
Sum of exterior angles of a polygon =
Exterior angles of 15 sided polygon
Hence, a
Question 4: Hoof w many sides does a regular polygon have if each of its interior angles is 165°?
Answer:
The measure of each interior angle is 165°
So, measure of each exterior angle = 180°-165° = 15°
Regular polygons have regular exterior angles equal.
Let the number of sides the the s of the polygon = n
The sum of the Exterior angles of a polygon =
Hence, a regular polygon having each of its interior angles is 165° has 24 sides.
Question 5 (a): Is it possible to have a regular polygon with a measure of each exterior angle of 22°?
Answer:
The measure of an exterior angle is 22°
A regular polygon has all exterior angles equal.
Sum of exterior angles of a polygon =
Let the number of sides be X.
Sum of exterior angles of a polygon =
Exterior angles of 15 sided polygon
Hence, the side of a polygon should be an integer but as shown ,above, the side is not an integer. So,it is not poss ible to have a regular polygon with the measure of each exterior angle as 22 o .
Question 5 (b): Can it be an interior angle of a regular polygon? Why?
Answer:
The measure of an interior angle is 22°
A regular polygon has all interior angles equal.
Let the number of sides and the number of interior angles be n.
Sum of interior angles of a polygon =
Sum of interior angles of a polygon =
The number of sides of a polygon should be an integer, but it is not an integer. So, it cannot be a regular polygon with an interior angle of 22 o
Question 6 (a): What is the minimum interior angle possible for a regular polygon? Why?
Answer:
Consider a polygon with the lowest number of sides, i.e., 3.
Sum of interior angles of 3 sided polygon =
Interior angles of a regular polygon are equal = A.
Hence, the minimum interior angle possible for a regular polygon is
Question 6 (b): What is the maximum exterior angle possible for a regular polygon?
Answer:
Let there be a polygon with the minimum number of sides, i.e., 3.
The exterior angles s an equilateral triangle have a maximum measure.
Sum of exterior angles of polygon =
Let the exterior angle be A.
Hence, the maximum exterior angle possible for a regular polygon is
Class 8 Maths Chapter 3 Question Answer: 3.3 Total Questions: 12 Page number: 30-32 |
Question 1 (i): Given a parallelogram ABCD. Complete each statement along with the definition or property used.
Answer:
In a parallelogram, opposite sides are equal in length.
Hence,
Question 1 (ii): Given a parallelogram ABCD. Complete each statement along with the definition or property used.
Answer:
In a parallelogram, opposite angles are equal.
(ii)
Question 1 (iii): Given a parallelogram ABCD. Complete each statement along with the definition or property used.
Answer:
In a parallelogram, both diagonals bisect each other.
Question 1 (iv): Given a parallelogram ABCD. Complete each statement along with the definition or property used.
Answer:
In a parallelogram, adjacent angles are supplementary to each other.
(iv)
Question 2 (i): Consider the following parallelograms. Find the values of the unknowns
Answer:
In a parallelogram, adjacent angles are supplementary to each other.
Opposite angles are equal.
Hence, z =
and y = 100
Question 2 (ii): Consider the following parallelograms. Find the values of the unknowns
Answer:
x=y=
z=x=
Question 2 (iii): Consider the following parallelograms. Find the values of the unknowns $x, y, z.
Answer:
x=
y=z=
Question 2 (iv): Consider the following parallelograms. Find the values of the unknowns
Answer:
y =
z=
Question 2 (v): Consider the following parallelograms. Find the values of the unknowns
Answer:
y =
x = z =
Question 3 (i): Can a quadrilateral ABCD be a parallelogram if
Answer:
(i)
Opposite angles should be equal, and adjacent angles should be supplementary to each other.
Hence, a quadrilateral ABCD can be a parallelogram, but it is not confirmed.
Question 3 (ii): Can a quadrilateral ABCD be a parallelogram if
Answer:
Opposite sides of a parallelogram are equal in length.
Since
No, it is not a parallelogram.
Question 3 (iii): Can a quadrilateral ABCD be a parallelogram if
Answer:
Opposite angles of a parallelogram are equal
Since here
So, it is not a parallelogram.
Answer:
The above-shown figure shows two opposite angles are equal.
But, it's not a parallelogram because the other two angles are different, i.e., $\angle A\neq \angle C.
Answer:
The measures of two adjacent angles of a parallelogram are in the ratio 2.
The sum of the adjacent angles is
Hence, angles are
Let there be a parallelogram ABCD, then,
Answer:
Given: Two adjacent angles of a parallelogram have equal measure =
Hence,
Answer:
The adjacent figure HOPE is a parallelogram.
y=
Question 8 (i): The following figures, GUNS and RUNS, are parallelograms. Find
Answer:
GUNS is a parallelogram, so opposite sides are equal in length
Hence,
Question 8 (ii): The following figures, GUNS and RUNS, are parallelograms. Find
Answer:
Diagonals of a parallelogram intersect each other.
Hence,
Question 9: In the above figure, both RISK and CLUE are parallelograms. Find the value of
Answer:
Question 10: Explain how this figure is a trapezium. Which of its two sides is parallel? (Fig. 3.26)
Answer:
Given,
A transverse line is intersecting two lines such that the sum of angles on the same side of the transversal line is
And hence, lines KL and MN are parallel to each other.
Quadrilateral KLMN has a pair of parallel lines, so it is a trapezium.
Question 11: Find
Answer:
Given ,
Hence,
Question 12: Find the measure of
(If you find
Answer:
Given,
Yes, to find
PQRS is a quadrilateral, so the sum of all angles is 360
and we know
so put values of
Class 8 Maths Chapter 3 Question Answer: 3.4 Total Questions: 6 Page number: 35 |
Question 1 (a): State whether True or False. All rectangles are squares
Answer:
(a) False, all squares are rectangles, but all rectangles can be squares.
Question 1 (b): State whether True or False. All rhombuses are parallelograms
Answer:
True. The opposite sides of the rhombus are parallel and equal.
Question 1 (c): State whether True or False. All squares are rhombuses and also rectangles.
Answer:
True. All squares are rhombuses because rhombuses have opposite sides parallel and equal, and same square has.
Also, all squares are rectangles because they have all interior angles of
Question 1 (d): State whether True or False. Not all squares are not parallelograms.
Answer:
False.
All squares have their opposite sides equal and parallel. Hence, they are parallelograms.
Question 1 (e): State whether True or False. All kites are rhombuses.
Answer:
False,
Kites do not have all sides equal, so they are not rhombuses.
Question 1 (f): State whether True or False. All rhombuses are kites.
Answer:
True, all rhombuses are kites because they have two adjacent sides equal.
Question 1 (g): State whether True or False. All parallelograms are trapeziums.
Answer:
True, all parallelograms are trapeziums because they have a pair of parallel sides.
Question 1 (h): State whether True or False. All squares are trapeziums.
Answer:
True, all squares are trapeziums because all squares have pairs of parallel sides.
Question 2 (a): Identify all the quadrilaterals that have four sides of equal length.
Answer:
The quadrilateral having four sides of equal length is are square and a rhombus.
Question 2 (b): Identify all the quadrilaterals that have four right angles
Answer:
All the quadrilaterals that have four right angles are rectangles and squares
Question 3 (i): Explain how a square is a quadrilateral
Answer:
A square is a quadrilateral because a square has four sides.
Question 3 (ii): Explain how a square is a parallelogram
Answer:
A square is a parallelogram because the square has opposite sides are parallel to each other.
Question 3 (iii): Explain how a square is a rhombus
Answer:
A square is a rhombus because a square has four sides equal.
Question 3 (iv): Explain how a square is a rectangle
Answer:
A square is a rectangle since it has all interior angles of
Question 4 (i): Name the quadrilaterals whose diagonals bisect each other
Answer:
The quadrilaterals whose diagonals bisect each other are a square, a rectangle, a parallelogram, and a rhombus.
Question 4 (ii): Name the quadrilaterals whose diagonals are perpendicular bisectors of each other.
Answer:
The quadrilaterals whose diagonals are perpendicular bisectors of each other are a rhombus and a square.
Question 4 (iii): Name the quadrilaterals whose diagonals are equal
Answer:
The quadrilaterals whose diagonals are equal are squares and rectangles.
Question 5: Explain why a rectangle is a convex quadrilateral.
Answer:
A rectangle is a convex quadrilateral because it has two diagonals and both lie in the interior of the rectangle.
Answer:
Draw line AD and DC such that
ABCD is a rectangle as it has opposite sides equal and parallel.
All angles of the rectangle are
Hence, AO = BO = CO = DO
The topics discussed in the NCERT Solutions for class 8, chapter 3, Understanding Quadrilaterals, are:
A closed two-dimensional figure composed of a finite number of straight line segments connected end to end is called a polygon. These line segments are called the sides of a polygon. The point where two line segments meet is called a corner or a vertex.
Polygons can be regular or irregular.
Triangles, squares, and rectangles are some of the examples of polygon.
Quadrilaterals are an important part of geometry, having four sides. There are some important quadrilaterals, i.e. squares, rectangles, trapezium, rhombus, and parallelograms. A quadrilateral also has four angles, four vertices, 12 edges, and two diagonals.
There are several formulas in geometry to calculate the area and parameters of the quadrilaterals.
We at Careers360 compiled all the NCERT class 8 Maths solutions in one place for easy student reference. The following links will allow you to access them.
Constructing a Quadrilateral
are the important topics of this chapter.
There are 16 chapters starting from rational number to playing with numbers in the CBSE class 8 maths.
No, CBSE doesn’t provide NCERT solutions for any class or subject.
Here you will get the detailed NCERT solutions for class 8 by clicking on the link.
NCERT solutions are provided in a very detailed manner which will give the conceptual clarity to the students. Also, students can take help from these solutions when they are not able to solve them on their own.
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