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All questions of Understanding Quadrilaterals for Class 8 Exam

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The ratio of two sides of a parallelogram is 4 : 3. If its perimeter is 56 cm, what is the difference between largest and smallest side?
  • a)
    8 cm
  • b)
    4 cm 9
  • c)
    12 cm
  • d)
    16 cm
Correct answer is option 'B'. Can you explain this answer?

Amit Sharma answered
The opposite sides of parallelogram are equal.
∴ 4x + 3x + 4x + 3x = 56
⇒ 14x = 56 ⇒ x = 4
∴ 4x = 4 × 4 = 16
and 3x = 4 × 3 = 12
∴ Difference = 16 – 12 = 4 cm

In ∆BCE, BE = EC, and ABCD is a square, and ∠BEC = 60°, then the measure of ∠BEA will be : 
  • a)
    45°
  • b)
    35°
  • c)
    15°
  • d)
    25°
Correct answer is option 'C'. Can you explain this answer?

Learning Education answered
Given BE = EC
∴ ∠EBC = ∠ECB
In ∆BEC,
2∠EBC + ∠BEC = 180°
⇒ ∠EBC = ∠ECB = 60°
∴ ∆EBC is an equilateral triangle having
EB = BC = EC
AB = BC = CD = DA = EB = EC
[∵ABCD is a square].
∠ABE = 90° + 60° = 150°
In ∆ABE,
∠ABE + 2∠AEB = 180° [Q AEB =  BAE].
2∠AEB = 180° - ∠ABE = 180 - 150 = 30°
⇒ ∠AEB = 15°

The four angles of a quadrilateral are in the ratio 2 : 3 : 5 : 8. Then what is the difference between largest and smallest angle of the quadrilateral?
  • a)
    80°
  • b)
    100°
  • c)
    110°
  • d)
    120°
Correct answer is option 'D'. Can you explain this answer?

Pooja Shah answered
Let the angles are 2x, 3x, 5x, 8x.
∴ 2x + 3x + 5x + 8x = 360°
⇒ 18x = 360° ⇒ x = 20°
2x = 2 × 20° = 40°; 3x = 3 × 20° = 60°
5x = 5 × 20° = 100°; 8x = 8 × 20° = 160°
Required difference = 160° - 40° = 120°.

If α < 90°, then, ABCD, may be a : (Given : ABCD is a parallelogram) and ∠B = 90°
  • a)
    Rectangle
  • b)
    Trapezium
  • c)
    Square
  • d)
    Rhombus
Correct answer is option 'A'. Can you explain this answer?

Geetika Shah answered
∵ ∠B = 90°, and, ABCD is a parallelogram
∴ ∠C = 90°, ∠A = 90° and ∠D = 90°
So, ABCD may be a rectangle or square, but, since, α < 90°.
∴ΑΒCD must be a rectangle.

If θ = 90°, and, ∠A = ∠C = 110°, then, ABCD is :
  • a)
    Square
  • b)
    Rectangle
  • c)
    Rhombus
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Shubham Sharma answered
∵ θ = 90° (Angle between the diagonals)
∴ ABCD may be a rhombus or square.
But, since, ∠A = ∠C = 110°
∴ ABCD must be a rhombus.
 In a rhombus or any parallelogram, the opposite angles are always equal 

From the adjoining figure, find the measure of ∠EFD if AB || CD, EF || BC.
  • a)
    40°
  • b)
    70°
  • c)
    50°
  • d)
    60°
Correct answer is option 'D'. Can you explain this answer?

Ananya Das answered
∠ABC + ∠BCF = 180°
[Interior angles or same side of transversal].
⇒ ∠BCF =180° - 120° = 60°
∠BCF = ∠EFD (corresponding angles)
∴ ∠EFD = 60°

In the adjoining figure, AD || BC and AB and DC are not parallel, then ∠B =
  • a)
    110°
  • b)
    70°
  • c)
    80°
  • d)
    40°
Correct answer is option 'B'. Can you explain this answer?

Geetika Shah answered
∵ AB is parallel to BC, and, AB is transversal.
∴ ∠A + ∠B = 180°
⇒ ∠B = 180° - ∠A = 180° - 110° = 70°

Find x and y:

KLMN is a parallelogram.
  • a)
    x = 55°, y = 55°
  • b)
    x = 65°, y = 55°
  • c)
    x = 60°, y = 65°
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Kavya Saxena answered
In ∆LAM, 
∠ALM + 90° + ∠M = 180°
⇒∠M = 65°
∴x=∠M= 60°  (∵KLMN is a parallelogram).
In ∆BLK,
∠BLK + 65° + 90° = 180°
⇒ ∠M = 180° - 90° = 90°
⇒∠BLK = 25°
∵ ∠L = 180° - 65° = y + 25° + 25°
⇒y = 65°

ABCD is an isosceles trapezium , i.e., AD = BC, then 
  • a)
    AD = CD
  • b)
    ∠A = ∠B
  • c)
    ∠A = ∠D
  • d)
    ∠C = ∠A 
Correct answer is option 'B'. Can you explain this answer?

Amit Sharma answered
∵ ABCD is an isosceles trapezium.
∴ AD = BC

Draw AE ⊥ DC and BF ⊥ DC, then, in ∆AED and ∠BFC.
∠AED = ∠BFC =  90°,
AB = BC,
AE = BF (perpendicular distance between two parallel lines)
∴ ∆AEB ≅ ∆BFC (ets congruency)
∴ ∠A = ∠B

ABCD is a rhombus and ∠AEF = 50°. Find x.
  • a)
    15°
  • b)
    20°
  • c)
    35°
  • d)
    25°
Correct answer is option 'D'. Can you explain this answer?

Target Study Academy answered
∵ AE = EB.
∴ ∠BAE = ∠ABE = x.
∵ ΔDO = OB, and , AO = OC
In ΔABE,
∠DAE + ∠ABE = ∠AEF
⇒ x + x = 50°
⇒ 2x = 50°
⇒ x = 25°

The quadrilateral formed by joining the mid-points of a given quadrilateral will be (surely) :
  • a)
    Parallelogram
  • b)
    Rectangle
  • c)
    Rhombus
  • d)
    Square 
Correct answer is option 'A'. Can you explain this answer?

Anika Bhatia answered

ABCD is a parallelogram and P,Q,R,S are the midpoints of AB, BC, CD, DA respectively. Consider, AC as a diagonal of ABCD.
Now, According to midpoint theorem,
PQ =1/2 AC and PQ is parallel to AC,
and SR = 1/2 AC and PQ is parallel to AC.
∴ PQ = RS and PQ || RS || AC.
∴ PQRS will be a parallelogram. 

ABCD is a rhombus and ABEF is a square find ‘a’.
  • a)
    30°
  • b)
    45°
  • c)
    60°
  • d)
    75°
Correct answer is option 'A'. Can you explain this answer?

Samarth Goyal answered
∵ AB is a common side in both square and rhombus.
∴ AB = BC = CD = DA = FA = FE = EB
In ∆EBC,
∠BEC + ∠C + ∠B = 180° [∠C = ∠BEC]
[∵ EB = BC]

[∠B = 90° + 60° = 150°]
∵ AE is the diagonal of square. ∴
∴∠AEF = 45°
Now,
∵∠ E is the angle of a square, 
∴∠E = 90°
⇒ 45° + 15° + a = 90°
⇒ a = 30°

The bisectors of any two adjacent angles of a parallelogram intersect at
  • a)
    30°
  • b)
    45°
  • c)
    60°
  • d)
    90°
Correct answer is option 'D'. Can you explain this answer?

Aarav Chaudhary answered
The Angle Properties of a Parallelogram
In a parallelogram, opposite angles are equal, and consecutive angles are supplementary (they add up to 180°).

Understanding the Angles
Let’s denote the angles of a parallelogram as A, B, C, and D. Then, we have:
- Angle A = Angle C
- Angle B = Angle D
- A + B = 180°

The Bisectors of Adjacent Angles
Now, consider two adjacent angles, say Angle A and Angle B. Their measures can be expressed as:
- A + B = 180°
When we draw the bisectors of these angles, they divide each angle into two equal parts:
- Angle A is divided into A/2 and A/2
- Angle B is divided into B/2 and B/2

Finding the Measure of the Angle Between the Bisectors
The angle between the two bisectors can be calculated as follows:
- Angle between bisectors = (A/2) + (B/2)
Substituting B = 180° - A, we get:
- Angle between bisectors = (A/2) + ((180° - A)/2)
This simplifies to:
- Angle between bisectors = (A + 180° - A)/2 = 180°/2 = 90°

Conclusion
Thus, the angle formed by the intersection of the bisectors of any two adjacent angles of a parallelogram is always 90°. Therefore, the correct answer is option 'D' - 90°.

In the above figure, OS = OQ and PR = 2OR = 2OR, and also, OR = OS, then, PQRS is not a
  • a)
    Rhombus
  • b)
    Rectangle
  • c)
    Square
  • d)
    Parallelogram.
Correct answer is option 'A'. Can you explain this answer?

Naveen Nair answered
∵ O is the bisector of both the diagonals.
∴ PQRS is a parallelogram.
∵ Diagonals of the parallelogram are equal. 
∴ PQRS may be a square or rectangle.

Chapter doubts & questions for Understanding Quadrilaterals - Mathematical Olympiad Class 8 2026 is part of Class 8 exam preparation. The chapters have been prepared according to the Class 8 exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Class 8 2026 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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