Chapter Exam

Chapter-4 Quadrilaterals — Online MCQ Test

Q: A quadrilateral is a polygon with how many sides?

Answer: B. 4 sides — By definition, a quadrilateral is a polygon with exactly 4 sides and 4 vertices.

Q: What is the sum of all interior angles of a quadrilateral?

Answer: C. 360° — The angle sum property of a quadrilateral states that the sum of all interior angles is always 360°.

Q: A convex polygon is one where:

Answer: B. All interior angles are less than 180° — In a convex polygon, all interior angles are less than 180°, and all diagonals lie inside the polygon.

Q: How many diagonals does a quadrilateral have?

Answer: B. 2 diagonals — A quadrilateral has exactly 2 diagonals, which connect opposite vertices.

Q: If three angles of a quadrilateral are 85°, 95°, and 100°, what is the fourth angle?

Answer: B. 80° — Using the angle sum property: Fourth angle = 360° - (85° + 95° + 100°) = 360° - 280° = 80°.

Q: In a parallelogram ABCD, if angle A = 65°, what is angle B?

Answer: B. 115° — In a parallelogram, consecutive angles are supplementary (sum to 180°). Therefore, angle B = 180° - 65° = 115°.

Q: In quadrilateral ABCD, if the diagonals AC and BD bisect each other, which type of quadrilateral must it be?

Answer: C. A parallelogram — The key property that diagonals bisect each other is characteristic of a parallelogram; other quadrilaterals may not have this property.

Q: A quadrilateral has vertices A, B, C, D where AB || DC and AB = DC. Which of the following must be true?

Answer: C. ABCD is a parallelogram — If one pair of opposite sides is both parallel and equal, the quadrilateral is a parallelogram. The other properties vary.

Q: In a kite ABCD with AB = AD and CB = CD, if angle BAD = 80°, angle BCD can be determined to be:

Answer: D. Cannot be determined without more information — In a kite, knowing one angle is insufficient. The angles depend on the specific dimensions. Angle BCD cannot be uniquely determined from angle BAD alone.

Q: A quadrilateral has angles in the ratio 1:2:2:3. The largest angle is:

Answer: C. 135° — Let angles be x, 2x, 2x, 3x. Sum: x + 2x + 2x + 3x = 8x = 360°, so x = 45°. Largest angle = 3x = 135°.

MATHS (KANITHA PRAKASH) · CLASS 8th · Karnataka State Board

Practice Chapter-4 Quadrilaterals with a free chapter-wise online MCQ test for Karnataka State Board CLASS 8th MATHS (KANITHA PRAKASH). This chapter covers: polygons - diagonals - convex polygon - concave polygon - regular polygon - angle sum property - parallelogram - rhombus - rectangle - square - kite. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter-4 Quadrilaterals — Important Questions & Answers (FAQ)

Frequently asked questions from Karnataka State Board CLASS 8th MATHS (KANITHA PRAKASH) — Chapter-4 Quadrilaterals, with answers and explanations. These are sample questions; the exam has its own separate question set.

A quadrilateral is a polygon with how many sides?

A. 3 sides
B. 4 sides ✓
C. 5 sides
D. 6 sides

Answer: B. 4 sides
By definition, a quadrilateral is a polygon with exactly 4 sides and 4 vertices.

What is the sum of all interior angles of a quadrilateral?

A. 180°
B. 270°
C. 360° ✓
D. 540°

Answer: C. 360°
The angle sum property of a quadrilateral states that the sum of all interior angles is always 360°.

A convex polygon is one where:

A. All interior angles are greater than 180°
B. All interior angles are less than 180° ✓
C. At least one interior angle is greater than 180°
D. Diagonals lie outside the polygon

Answer: B. All interior angles are less than 180°
In a convex polygon, all interior angles are less than 180°, and all diagonals lie inside the polygon.

How many diagonals does a quadrilateral have?

A. 1 diagonal
B. 2 diagonals ✓
C. 3 diagonals
D. 4 diagonals

Answer: B. 2 diagonals
A quadrilateral has exactly 2 diagonals, which connect opposite vertices.

If three angles of a quadrilateral are 85°, 95°, and 100°, what is the fourth angle?

A. 70°
B. 80° ✓
C. 85°
D. 90°

Answer: B. 80°
Using the angle sum property: Fourth angle = 360° - (85° + 95° + 100°) = 360° - 280° = 80°.

In a parallelogram ABCD, if angle A = 65°, what is angle B?

A. 65°
B. 115° ✓
C. 125°
D. 155°

Answer: B. 115°
In a parallelogram, consecutive angles are supplementary (sum to 180°). Therefore, angle B = 180° - 65° = 115°.

In quadrilateral ABCD, if the diagonals AC and BD bisect each other, which type of quadrilateral must it be?

A. A kite
B. A trapezium
C. A parallelogram ✓
D. A rectangle

Answer: C. A parallelogram
The key property that diagonals bisect each other is characteristic of a parallelogram; other quadrilaterals may not have this property.

A quadrilateral has vertices A, B, C, D where AB || DC and AB = DC. Which of the following must be true?

A. ABCD is a rectangle
B. ABCD is a rhombus
C. ABCD is a parallelogram ✓
D. ABCD is a kite

Answer: C. ABCD is a parallelogram
If one pair of opposite sides is both parallel and equal, the quadrilateral is a parallelogram. The other properties vary.

In a kite ABCD with AB = AD and CB = CD, if angle BAD = 80°, angle BCD can be determined to be:

A. 80°
B. 100°
C. 160°
D. Cannot be determined without more information ✓

Answer: D. Cannot be determined without more information
In a kite, knowing one angle is insufficient. The angles depend on the specific dimensions. Angle BCD cannot be uniquely determined from angle BAD alone.

A quadrilateral has angles in the ratio 1:2:2:3. The largest angle is: