Geometry is one of the basic topics in mathematics, where students studies different geometrical shapes and figures, and understand their key properties and usage in real life. This chapter on understanding quadrilaterals cover the studies of polygons like what they are , angle sum properties, their basic properties etc. It will cover polygons with 4 sides which are also called quadrilaterals . It also cover special cases like trapezium, and cover their properties as well.

Grade 8 understanding quadrilaterals chapter covers the detailed coverage of this topic, including studying its properties, and then solving to get the value of unknown variable. This chapter has been best covered in Class 8 Maths NCERT book, which give real life examples of polygons, quadrilaterals and trapezium, and cover all the sections thoroughly.

NCERT books are recommended course text books for students following Indian curriculum. They have been followed by CBSE and all other major school boards in India and abroad. Almost all of the public and private schools recommend this books to their students.

In this article, we have discussed about the Class 8 maths NCERT exercises. We have provided detailed video solutions of NCERT problems for Class 8. Students can look into solved NCERT exercises for class 8 mathematics.

Though understanding quadrilaterals chapter looks easy, but many students make mistake in understanding properties of polygons and quadrilaterals . These solved NCERT problems for class 8 will help in clearing the concepts of rational numbers, and also make student understand in how to avoid common mistakes in linear equations in one variable chapters.

## Class 8 math ncert solution understanding quadrilaterals chapter

**Exercise 3.1 solutions**

Q1 – Given here are some figures. Classify each of them on the basis of the following (a) Simple curve (b) Simple closed curve (c) Polygon(d) Convex polygon (e) Concave polygon View Answer

Q2 – How many diagonals does each of the following have? (a) A convex quadrilateral (b) A regular hexagon (c) A triangle View Answer

Q3 – What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make anon-convex quadrilateral and try!) View Answer

Q4 – Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.) What can you say about the angle sum of a convex polygon with number of sides?(a) 7 (b) 8 (c) 10 (d) n View Answer

Q5 – What is a regular polygon? State the name of a regular polygon of (i) 3 sides (ii) 4 sides (iii) 6 sides View Answer

Q6 – Find the angle measure x in the following figures View Answer

Q7 – (a) Find x + y + z (b) Find x + y + z + w View Answer

**Exercise 3.2**

Q1 – Find x in the following figures View Answer

Q2 – Find the measure of each exterior angle of a regular polygon of (i) 9 sides (ii) 15 sides View Answer

Q3 – How many sides does a regular polygon have if the measure of an exterior angle is 24°? View Answer

Q4 – How many sides does a regular polygon have if each of its interior angles is 165°? View Answer

Q5 – (a) Is it possible to have a regular polygon with measure of each exterior angle as 22°? (b) Can it be an interior angle of a regular polygon? Why? View Answer

Q6 – (a) What is the minimum interior angle possible for a regular polygon? Why? (b) What is the maximum exterior angle possible for a regular polygon? View Answer

**Exercise 3.3**

Q1 – Given a parallelogram ABCD. Complete each statement along with the definition or property used. (i) AD = …… (ii) ∠ DCB = …… (iii) OC = …… (iv) m ∠DAB + m ∠CDA = …. View Answer

Q2 – Consider the following parallelograms. Find the values of the unknowns x, y, z. View Answer

Q3 – 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°? View Answer

Q4 – Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure. View Answer

Q5 – 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. View Answer

Q6 – Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram. View Answer

Q7 – The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them. View Answer

Q8 – The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm) View Answer

Q9 – In the above figure both RISK and CLUE are parallelograms. Find the value of x. View Answer

Q10 – Explain how this figure is a trapezium. Which of its two sides are parallel? View Answer

Q11 – Find m∠C if AB parallel to DC . View Answer

Q12 – Find the measure of ∠P and ∠S if SP parallel to RQ. (If you find m∠R, is there more than one method to find m∠P?) View Answer

**Exercise 3.4**

Q1 – State whether True or False. (a) All rectangles are squares (e) All kites are rhombuses. (b) All rhombuses are parallelograms (f) All rhombuses are kites. (c) All squares are rhombuses and also rectangles (g) All parallelograms are trapeziums.(d) All squares are not parallelograms. (h) All squares are trapeziums. View Answer

Q2 – Identify all the quadrilaterals that have. (a) four sides of equal length (b) four right angles View Answer

Q3 – Explain how a square is. (i) a quadrilateral (ii) a parallelogram (iii) a rhombus (iv) a rectangle View Answer

Q4 – Name the quadrilaterals whose diagonals. (i) bisect each other (ii) are perpendicular bisectors of each other (iii) are equal View Answer

Q5 – Explain why a rectangle is a convex quadrilateral. View Answer

Q6 – ABC is a right-angled triangle and O is the mid point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you). View Answer

## End Note

In the article, we have shared solutions for ncert exercises for class 8 maths for understanding quadrilaterals chapter. Students can click to respective chapters and refer to the right solution. We advise students to refer to them as clearing their concepts, and matching their solutions. Student should not use them to copy solutions for their homework and instead should try to solve homework on own, as it will impact their learning process.

In case you have any doubts regarding solution, or need further clarification, you can write to us. You can also reach out to us, in case you have doubt in other text books’ problems or school exam papers. We will be glad to assist you in helping with your doubt.

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