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Class 8 Maths: Quadrilaterals, 8 practice questions with answers
These are 8 practice questions on Chapter 4, Quadrilaterals, of the new NCERT Class 8 Maths textbook, Ganita Prakash, Part 1. Each has a worked answer and the textbook page it comes from. They cover finding an unknown from the angle sum, when a pair of diagonals proves a rectangle, spotting a mistake in a parallelogram's angles, the diagonals of a kite, which quadrilaterals have perpendicular diagonals, a square's diagonals, the sides of a parallelogram from its perimeter, and why a parallelogram's diagonals need not be equal. Try each one on paper before you open the answer.
These questions are our own, drafted with AI help. Every number was re-computed by a test script and none of the numbers is taken from the chapter, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.
What the chapter says you need
Facts from the NCERT textbook (Ganita Prakash, Grade 8, Part 1, Chapter 4, printed pages 82 to 110):
- The angles of any quadrilateral add up to 360° (page 95).
- A rectangle is a quadrilateral whose angles are all 90°; its opposite sides are equal and parallel, and its diagonals are equal and bisect each other. A quadrilateral whose diagonals are equal and bisect each other is a rectangle (pages 84 to 90).
- A square is a rectangle with all sides equal; its diagonals are equal, bisect each other at 90°, and bisect the angles of the square, making 45° with the sides (pages 91 to 93).
- In a parallelogram, opposite sides are equal, adjacent angles add up to 180°, opposite angles are equal, and the diagonals bisect each other; the diagonals need not be equal (pages 96 to 99).
- In a kite ABCD with AB = BC and CD = DA, the diagonal BD bisects the diagonal AC and is perpendicular to it (page 105).
Angles and diagonals
Question 1. The four corners of a farm plot measure x°, (x + 25)°, (x + 67)° and (2x + 8)°. Find x and all four angles.
Answer: x = 52; the angles are 52°, 77°, 119° and 112°. The angles of a quadrilateral add up to 360°: x + (x + 25) + (x + 67) + (2x + 8) = 360, so 5x + 25 + 67 + 8 = 360 and 5x = 260, giving x = 52. The angles are 52°, 52 + 25 = 77°, 52 + 67 = 119° and 2 × 52 + 8 = 112°. Check: 52 + 77 + 119 + 112 = 360. (Angle sum of a quadrilateral, page 95.)
Question 2. A mason marks out a floor with four pegs and two strings joining opposite pegs. Both strings measure 7.4 m, but they cross at a point that is not the midpoint of either string. Can she be sure the floor is a rectangle? What if, instead, the strings measured 7.4 m and 7.6 m and crossed exactly at their midpoints?
Answer: no in both cases. A quadrilateral is a rectangle when its diagonals are equal and bisect each other. In the first case the strings are equal but do not bisect each other, so that test fails and she cannot be sure of a rectangle. In the second case the strings bisect each other, so the floor is a parallelogram, but they are not equal, so it is not a rectangle. (Rectangles and their diagonals, pages 88 and 89; diagonals that bisect each other, Figure it Out 11(iii), page 109.)
Question 3. Ravi says the angles of a parallelogram are 64°, 116°, 64° and 126°. Show that this is impossible and correct the mistake.
Answer: the fourth angle must be 116°, not 126°. In a parallelogram, opposite angles are equal and adjacent angles add up to 180°. The angle opposite 116° must also be 116°, and 64° + 116° = 180° as it should be. Ravi's angles add up to 64 + 116 + 64 + 126 = 370°, but the angles of a quadrilateral add up to 360°, so his set cannot be right. (Angles of a parallelogram, page 97; angle sum, page 95.)
Question 4. A kite (patang) is made from two sticks. The cross stick AC is 58 cm long, and the long stick BD is tied across it so that AB = BC and CD = DA. Where does BD cross AC, and at what angle?
Answer: at the midpoint of AC, 29 cm from each end, at 90°. In a kite ABCD with AB = BC and CD = DA, the diagonal BD bisects AC and is perpendicular to it. So BD crosses AC at its midpoint, with AO = OC = 58 ÷ 2 = 29 cm, and the angle between the sticks is 90°. (Kite, page 105.)
Sides and diagonals
Question 5. Which of these must have diagonals that cross at 90°: a rectangle with sides 117 cm and 44 cm, a rhombus with sides 44 cm, or a parallelogram with sides 117 cm and 44 cm? Explain.
Answer: only the rhombus. The diagonals of a rhombus always intersect at 90°, because the two triangles on either side of one diagonal are congruent and the two angles at the crossing add up to 180°. A rectangle's diagonals are equal and bisect each other, but they cross at 90° only when it is a square, and a 117 cm by 44 cm rectangle is not a square. A parallelogram's diagonals bisect each other, but they need not be perpendicular. (Diagonals of a rhombus, page 102; rectangles, page 90; parallelograms, page 99.)
Question 6. A square courtyard has a diagonal of 46 m. A lamp post stands where the two diagonals cross. How far is the post from each corner, at what angle do the diagonals cross, and what angle does each diagonal make with a side?
Answer: 23 m from each corner; 90°; 45°. The diagonals of a square are equal and bisect each other at 90°, so the post is 46 ÷ 2 = 23 m from every corner and the diagonals cross at 90°. They also bisect the 90° corners, so each makes 45° with a side. (Properties of a square, page 93.)
Question 7. A field shaped like a parallelogram has a perimeter of 238 m, and one side is 67 m. Find the other three sides.
Answer: 67 m, 52 m and 52 m. Opposite sides of a parallelogram are equal, so the sides are 67, a, 67 and a. Then 2 × (67 + a) = 238, so 67 + a = 119 and a = 52 m. The sides are 67 m, 52 m, 67 m and 52 m. (Opposite sides of a parallelogram, page 98.)
Question 8. Meena says, "My quadrilateral has diagonals of 74 cm and 52 cm that cross at their midpoints, so it can't be a parallelogram, because a parallelogram's diagonals are equal." Is she right? How long is each part of each diagonal?
Answer: no; it is a parallelogram, with parts 37 cm and 26 cm. Diagonals that bisect each other make a quadrilateral a parallelogram; they only need to be equal for a rectangle. The chapter notes that the diagonals of a parallelogram need not be equal. Each diagonal is cut in half: 74 ÷ 2 = 37 cm and 52 ÷ 2 = 26 cm. (Diagonals that bisect each other, Figure it Out 11(iii), page 109; diagonals of a parallelogram need not be equal, page 98; rectangles, page 89.)
Practise more, and check your marks
- Printable Class 8 worksheets with answer keys, in English, Hindi and Marathi: Class 8 worksheets.
- The chapter before this one: Class 8 A Story of Numbers.
- The chapter after this one: Class 8 Number Play.
- Where quadrilaterals go in Class 9: Class 9 Quadrilaterals.
- More geometry in Class 9: Class 9 Circles.
- Class 8 Science in the same style: Class 8 Force and Pressure.
Where CMDLearn fits
CMDLearn is building an AI tutor for Classes 1 to 10 that explains a step and checks the child's working, but leaves the writing to the child. It is still in development, and no child uses it yet. If you would like to hear when there is something to try, you can join the waitlist.
Sources
All opened and read on 22 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 81.
- NCERT, Ganita Prakash: Textbook of Mathematics for Grade 8, Part 1 (First Edition July 2025, Reprint 2026-27), Chapter 4 "Quadrilaterals", printed pages 82-110 (the rectangle and its diagonals, pages 84-90; the square, pages 91-93; the angle sum of a quadrilateral, page 95; the parallelogram's angles, sides and diagonals, pages 96-99; the kite, page 105; summary, pages 109-110): ncert.nic.in/textbook/pdf/hegp104.pdf
- NCERT, Ganita Prakash, Grade 8, Part 1, front matter (edition and reprint lines): ncert.nic.in/textbook/pdf/hegp1ps.pdf
The properties are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.