Quadrilaterals — Class 8 MCQs with Answers
Class 8 CBSE Mathematics · Chapter 4
72 practice questions · 24 Easy · 24 Medium · 24 Hard · Updated
Practise the most important Class 8 CBSE Mathematics questions from Chapter 4, "Quadrilaterals". You get 9 timed quizzes made from 72 NCERT-based MCQs, with answers and explanations. The questions are split into 24 Easy, 24 Medium and 24 Hard. Warm up on the basics, then move on to the exam-level questions that top scorers in CBSE Board exams get right.
To score well in "Quadrilaterals", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This helps you stay accurate when time is short, just as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on Quadrilaterals, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 8 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
Quadrilaterals — important questions & MCQs with answers (Class 8 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation.
- Q1Easy
Three angles of a quadrilateral are 90°, 90° and 90°. What is the fourth angle?
A.100°B.80°C.90°✓ CorrectD.110°Answer: C. 90°
Explanation: Three angles of 90° use 3 × 90° = 270° of the 360° total, leaving 360° − 270° = 90° for the fourth angle — not 100° or 80°.
- Q2Easy
A quadrilateral in which all four sides are equal but the angles need not be right angles is a:
A.rectangleB.rhombus✓ CorrectC.trapeziumD.kiteAnswer: B. rhombus
Explanation: A shape with all four sides equal, whatever its angles, is a rhombus by definition — a rectangle instead needs all angles equal to 90°.
- Q3Easy
In a rectangle, the two diagonals are:
A.perpendicularB.unequalC.curvedD.equal in length✓ CorrectAnswer: D. equal in length
Explanation: A defining property of a rectangle is that its two diagonals are always equal in length; they are perpendicular only if it is also a square.
- Q4Easy
A square is a special rectangle in which:
A.the angles are not right anglesB.there are no parallel sidesC.all sides are equal✓ CorrectD.there are five sidesAnswer: C. all sides are equal
Explanation: A square keeps a rectangle's 90° angles but adds the extra condition that all four sides are equal in length.
- Q5Easy
Three angles of a quadrilateral are 100°, 80° and 90°. What is the fourth angle?
A.100°B.80°C.90°✓ CorrectD.110°Answer: C. 90°
Explanation: The four angles of a quadrilateral sum to 360°. Here 100° + 80° + 90° = 270°, so the missing angle is 360° − 270° = 90°.
- Q6Easy
A quadrilateral with all right angles and opposite sides equal is a:
A.rectangle✓ CorrectB.rhombusC.kiteD.trapeziumAnswer: A. rectangle
Explanation: Four right angles with opposite sides equal is exactly the definition of a rectangle; a rhombus needs equal sides, not equal angles.
- Q7Medium
In a parallelogram, one angle is 70°. The angle opposite to it is:
A.110°B.90°C.140°D.70°✓ CorrectAnswer: D. 70°
Explanation: Opposite angles in a parallelogram are always equal, so the angle opposite a 70° angle is also 70° — not its supplement 110°.
- Q8Medium
In the kite ABCD, which sides are equal?
A.AB = BC and CD = DA✓ CorrectB.AB = CD and BC = DAC.all four sides are equalD.no sides are equalAnswer: A. AB = BC and CD = DA
Explanation: A kite has two pairs of equal ADJACENT sides, AB = BC and CD = DA — not opposite sides equal, which would describe a parallelogram instead.
- Q9Medium
In a rectangle, the diagonals:
A.are equal and bisect each other✓ CorrectB.are perpendicularC.are unequalD.do not intersectAnswer: A. are equal and bisect each other
Explanation: A rectangle's diagonals are always equal in length and always cut each other exactly in half — they are perpendicular only if it is also a square.
- Q10Medium
Every rectangle is a parallelogram because:
A.all its sides are equalB.its opposite sides are parallel and equal✓ CorrectC.its diagonals are perpendicularD.it has only one pair of parallel sidesAnswer: B. its opposite sides are parallel and equal
Explanation: A rectangle satisfies the parallelogram condition because its opposite sides are both parallel and equal in length, not because all four sides match.
- Q11Medium
In a parallelogram, one angle is 70°. An angle next to it (adjacent) is:
A.70°B.90°C.110°✓ CorrectD.80°Answer: C. 110°
Explanation: Adjacent angles in a parallelogram are supplementary, summing to 180°, so next to a 70° angle sits 180° − 70° = 110°.
- Q12Hard
In a parallelogram, two adjacent angles are (2x + 10)° and (3x)°. Find x.
A.30B.35C.44D.34✓ CorrectAnswer: D. 34
Explanation: Adjacent angles in a parallelogram sum to 180°: (2x + 10) + 3x = 180 gives 5x = 170, so x = 34.
- Q13Hard
A rhombus has each side 9 cm. Its perimeter is:
A.18 cmB.81 cmC.27 cmD.36 cm✓ CorrectAnswer: D. 36 cm
Explanation: All four sides of a rhombus are equal, so the perimeter is 4 × 9 = 36 cm, not 9² = 81 cm².
- Q14Hard
A rhombus has diagonals 6 cm and 8 cm. The length of each side is:
A.5 cm✓ CorrectB.7 cmC.10 cmD.14 cmAnswer: A. 5 cm
Explanation: The diagonals bisect each other at right angles into halves of 3 cm and 4 cm, so each side is √(3² + 4²) = √25 = 5 cm.
Key concepts: Quadrilaterals (Class 8 Mathematics)
This chapter defines the family of four-sided figures and the properties that tell them apart. The key result is that the four angles of any quadrilateral add up to 360°, proved by cutting it into two triangles with a diagonal. You define rectangle, square, parallelogram, rhombus, kite and trapezium, and — following the book's approach — learn to recognise each one from its diagonals: whether they are equal, whether they bisect each other, and whether they meet at right angles.
- Quadrilateral
- A closed figure with four sides, four angles and two diagonals. Its shape is fixed by the lengths of its sides and the sizes of its angles.
- Angle sum property
- The four angles of any quadrilateral always add up to 360°. A diagonal splits it into two triangles, and 2 × 180° = 360°.
- Rectangle
- A quadrilateral with four right angles and opposite sides equal. Its diagonals are equal in length and bisect each other.
- Square
- A rectangle whose sides are all equal — so it is both a rectangle and a rhombus. Its diagonals are equal and bisect each other at right angles.
- Parallelogram
- A quadrilateral with both pairs of opposite sides parallel. Opposite sides and opposite angles are equal, adjacent angles are supplementary, and the diagonals bisect each other.
- Rhombus
- A quadrilateral with all four sides equal. It is a parallelogram whose diagonals bisect each other at right angles but are usually unequal.
- Kite
- A quadrilateral with two pairs of equal adjacent sides (AB = BC, CD = DA). One diagonal is the perpendicular bisector of the other and bisects the vertex angles.
- Trapezium
- A quadrilateral with at least one pair of parallel opposite sides. The two angles on the same slant side (co-interior) add up to 180°.
- Diagonals as identifiers
- The book tells shapes apart by diagonals: equal + bisecting = rectangle, perpendicular + bisecting = rhombus, both together = square.
- Co-interior angles
- In a trapezium, a pair of angles between the two parallel sides on the same arm sums to 180°, letting you find unknown angles without measuring.
- Hierarchy of quadrilaterals
- A square is a special rectangle and a special rhombus; rectangles and rhombuses are special parallelograms; parallelograms are special trapeziums.
- Isosceles trapezium
- A trapezium whose two non-parallel (slant) sides are equal; its base angles are equal and its diagonals are equal in length.
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Start this chapter free →Quadrilaterals — FAQs
What are the key concepts in Class 8 Mathematics Quadrilaterals?+
This chapter defines the family of four-sided figures and the properties that tell them apart. The key result is that the four angles of any quadrilateral add up to 360°, proved by cutting it into two triangles with a diagonal. You define rectangle, square, parallelogram, rhombus, kite and trapezium, and — following the book's approach — learn to recognise each one from its diagonals: whether they are equal, whether they bisect each other, and whether they meet at right angles. Key ideas include Quadrilateral, Angle sum property, Rectangle, Square, Parallelogram, Rhombus.
What does Class 8 Mathematics Chapter 4 (Quadrilaterals) cover on XamBaaz?+
It has 72 NCERT-based MCQs on "Quadrilaterals": 24 Easy, 24 Medium and 24 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams.
Are these "Quadrilaterals" questions free to practise?+
Yes. Sign in with Google to practise "Quadrilaterals" free. Full unlimited access is ₹999/year. One year from the day you pay. You stay in Class 8 till 31 March; on 1 April your account moves up to Class 9 and the rest of your year carries over. No chapter is charged separately.
How should I revise "Quadrilaterals" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "Quadrilaterals" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "Quadrilaterals" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Quadrilaterals (Class 8 Mathematics)?+
The questions that matter most test Quadrilateral, Angle sum property, Rectangle, Square, Parallelogram, Rhombus. This page shows 14 solved important MCQs with answers and explanations. Sign in to practise all 72 questions on the chapter as timed quizzes.
Is there an online quiz for Quadrilaterals?+
Yes — Class 8 Mathematics Quadrilaterals has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.