Class 8th Mathematics MCQ

Q1. What is the name of a regular polygon of 4 sides?

1. Regular hexagon

2. Regular octagon

3. Square

4. Equilateral triangle

Ans: 3. Square

Q2. The kite has exactly two distinct consecutive pairs of sides of equal length.

1. False

2. True

Ans: 2. True

Solution:

A kite is a quadrilateral that has exactly two distinct consecutive pairs of sides of equal length.

Q3. The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a

rectangle if:

1. Diagonals of PQRS are perpendicular

2. PQRS is a rectangle

3. PQRS is a parallelogram

4. Diagonals of PQRS is equal

Ans: 1. Diagonals of PQRS are perpendicular

Q4. Which of the following statements is false?

1. All the angles of a rectangle are equal.

2. No angle of a rectangle can be obtuse.

3. The diagonals of a rectangle bisect each other.

4. The opposite sides of a rectangle are not equal

Ans: 4. The opposite sides of a rectangle are not equal.

Q5. One of the diagonals of a rhombus is equal to a side of the rhombus. The angles of the rhombus are:

1. 60º and 120º

2. 100º and 120º

3. 60º and 80º

4. 120º and 240º

Ans: 1. 60º and 120º

Q6. In a square ABCD, AB = (2x + 3)cm and BC = (3x – 5)cm. Then, the value of x is:

1. 4

2. 5

3. 6

4. 8

Ans: 4. 8

Solution:

We know, all sides are equal of a square. Then,

AB = BC

⇒ 2x + 3 = 3x – 5

⇒ 3x – 2x = 3 + 5

⇒ x = 8

Q7. The diagonals of a parallelogram ABCD, intersect at O. If and then, is:

1. 10º

2. 50º

3. 40º

4. 90º

Ans: 3. 40º

Q8. In a parallelogram Then,

1. 30º

2. 60º

3. 45º

4. 90º

Ans: 2. 60º

Solution:

Stun of the ratios = 1 + 2 = 3

Q9. If a diagonal of a quadrilateral bisects both the angles, then it is a:

1. kite

2. parallelogram

3. rhombus

4. rectangle

Ans: 3. rhombus

Solution:

If a diagonal of a quadrilateral bisects both the angles, then it is a rhombus.

Q10. A rhombus has a side length equal to 5cm. Find its perimeter.

1. 20

2. 30

3. 25

4. 10

Ans: 1. 20

Solution:

A rhombus is a parallelogram that has all its four sides equal. Thus, the perimeter of rhombus,

P = 4 × side-length

P = 4 × 5

P = 20cm

Q11. The sum of the measures of the exterior angles of any polygon is:

1. 90º

2. 180º

3. 360º

4. 720º

Ans: 3. 360º

Q12. A parallelogram PQRS is constructed with sides QR = 6cm, PQ = 4cm and ∠PQR = 90°. Then PQRS is a:

1. square

∴

∠BOC − 90∘ ∠BDC = 50∘ ∠AOB

∠A : ∠B = 1 : 2 ∠A =

∠A + ∠B = 180∘

∠A : ∠B = 1 : 2

∴ ∠A = 1 × 180∘ = 60∘

3

Q13. If PQRS is a parallelogram, then is equal to.

1. 60

2. 90

3. 80

4. 0

Ans: 4. 0°

Solution:

Since, in a parallelogram, opposite angles are equal. Therefore, , as, are opposite angles.

Q14. The sum of adjacent angles of a parallelogram is.

1. 180

2. 120

3. 360

4. 90

Ans: 1. 180

Solution:

By property of the parallelogram, we know that, the sum of adjacent angles of a parallelogram is 180 .

Q15. If and are two opposite angles of a parallelogram, then:

1.

2.

3.

4. None of the above

Ans: 1.

Solution:

Opposite angles of a parallelogram are always equal.

Q16. If the two angles of a triangle are 80º and 50º, respectively. Find the measure of the third angle.

1. 70º

2. 80º

3. 50º

4. 60º

Ans: 3. 50º

Solution:

By the angle sum property of triangle, we know that;

Sum of all the angles of a triangle = 180º

Let the unknown angle be x

80º + 50º + x = 180º

x = 180º – 130º

x = 50º

Q17. For which of the following, diagonals bisect each other?

1. Square

2. Kite

3. Trapezium

4. Quadrilateral

2. rectangle

3. rhombus

4. trapezium

Ans: 2. rectangle

Solution:

We know that, if in a parallelogram one angle is of 90 , then all angles will be of 90 and a parallelogram with all angles equal to 90 is

called a rectangle.

° ° °

∠P − ∠R

°

°

°

°

∠P − ∠R = 0 ∠P and ∠R

°

°

°

°

°

°

∠A ∠C

∠A = ∠C

∠A < ∠C

∠A > ∠C

∠A = ∠C

Ans: 1. Square

Solution:

We know that, the diagonals of a square bisect each other but the diagonals of kite, trapezium and quadrilateral do not bisect each

other.

Q18. What is the area of the rectangle whose perimeter is 16cm & length 5cm?

1. 3.2cm

2. 80cm

3. 15cm

4. 16cm

Ans: 3. 15cm

Q19. Tick the correct answer in the following?

The angles of a pentagon are xº, (x + 20)°, (x + 40)º, (x + 60)º and (x + 80)º. The smallest angle of the pentagon is:

1. 75º

2. 68º

3. 78º

4. 85º

Ans: 2. 68º

Solution:

(5 – 2) × 180º – x + x + 20 + x + 40 + x + 60 + x + 80

⇒ 540 – 5x + 200

⇒ 5x – 340

⇒ x – 68º

Q20. State the name of a regular polygon of 5 sides.

1. Hexagon

2. Quadrilateral

3. Pentagon

4. Heptagon

Ans: 3. Pentagon

Q21. If the adjacent angles of a parallelogram are equal, then the parallelogram is a:

1. rectangle

2. trapezium

3. rhombus

4. any of the three

Ans: 1. rectangle

Solution:

We know that, the adjacent angles of a parallelogram are supplementary, i.e. their sum equals 180 & given that both the angles are

same. Therefore, each angle will be of measure 90 . Hence, the parallelogram is a rectangle.

Q22. In a parallelogram ABCD, angle A and angle B are in the ratio 1 : 2. Find the angle A.

1. 60º

2. 90º

3. 30º

4. 45º

Ans: 1. 60º

Solution:

As we know, the sum of adjacent angles of a parallelogram is equal to 180º and opposite angles are equal to each other.

Thus, in parallelogram ABCD angle A and angle B are adjacent to each other

Let angle A = x and angle B = 2x.

So, x + 2x = 180º

3x = 180º

2

2

2

2

2

∴

°

°

x = 60º

Q23. If one angle of a parallelogram is 24º less than twice the smallest angle then the largest angle of the

parallelogram is:

1. 68º

2. 102º

3. 112º

4. 176º

Ans: 3. 112º

Solution:

Let the measure of smallest anlge be xº and other is (2x – 24)º.

x + (2x – 24) = 180

⇒ x + 2x = 180 + 24

⇒ 3x = 204

⇒ x = 68

Hence, the samllest angle is 68º.

Ite adjacent is = (180 – 68)º = 112º.

Therefore, the largest angle is 112º.

Q24. For which of the following figures, diagonals are perpendicular to each other?

1. Parallelogram

2. Kite

3. Trapezium

4. Rectangle

Ans: 2. Kite

Solution:

The diagonals of a kite are perpendicular to each other.

Q25. In a regular polygon of n sides, the measure of each internal angle is:

1.

2.

3. n 90º

4. 2n right angles

Ans: 2.

Q26. ABCD is a quadrilateral. If AC and BD bisect each other then ABCD must be:

1. Rectangle

2. The angle

3. Parallelogram

4. Square

Ans: 3. Parallelogram

Q27. What is the sum of all exterior angles of a pentagon?

1. 180º

2. 360º

3. 540º

4. 720º

Ans: 2. 360º

Solution:

We know that the sum of all exterior angles of a polygon is 360 degrees.

Q28. One angle of a parallelogram is a right angle. The name of the quadrilateral is:

1. Square

2. Rectangle

∴

360∘

n

( 2n – 4 )90∘

n

( 2n – 4 )90∘

n

3. Rhombus

4. Kite

Ans: 2. Rectangle

Q29. Tick the correct answer in the following?

The sum of all interior angles of a regular polygon is 1080º. What is the measure of each of its interior angles?

1. 135º

2. 120º

3. 156º

4. 144º

Ans: 1. 135º

Solution:

(2n – 4) × 90 = 1080

(2n – 4) = 12

2n = 16

Or n = 8

Each interior angle

Q30. The sum of the measures of all the four angles of a quadrilateral is:

1. 90º

2. 180º

3. 360º

4. 720º

Ans: 3. 360º

Q31. Find the measure of each exterior angle of a regular polygon of 9 sides.

1. 30º

2. 90º

3. 40º

4. 60º

Ans: 3. 40º

Q32. Two adjacent angles of a parallelogram are in the ratio 1:5. Then all the angles of the parallelogram are:

1. 30 , 150 , 30 , 150

2. 85 , 95 , 85 , 95

3. 45 , 135 , 45 , 135

4. 30 , 180 , 30 , 180

Ans: 1. 30 , 150 , 30 , 150

Solution:

Let the adjacent angles of a parallelogram be x and 5x, respectively.

Then, x + 5x = 180 [adjacent angles of a parallelogram are supplementary]

⇒ 6x = 180°

⇒ x = 30

Q33. If and are two adjacent angles of a parallelogram. If , then ?

1. 110º

2. 180º

3. 70º

4. 90º

Ans: 1. 110º

Solution:

The adjacent angles of parallelogram are supplementary.

= 180 − 360 = 180 − = 180 − 45 = 135∘

n

360

8

° ° ° °

° ° ° °

° ° ° °

° ° ° °

° ° ° °

°

°

∠A ∠B ∠A = 70∘, ∠B =

∠B + ∠B = 180∘

Q34. If one angle of a parallelogram is of 65º, then the measure of the adjacent angle is:

1. 65º

2. 115º

3. 25º

4. 90º

Ans: 2. 115º

Solution:

Measure of the adjacent angle

= 180º – 65º = 115º.

Q35. Each of the angles of a square is:

1. Obtuse angle

2. 180 degrees

3. Acute angle

4. Right angle

Ans: 4. Right angle

Solution:

All the angles of square is at right angle.

Q36. How many diagonals does a hexagon have?

1. 9

2. 8

3. 2

4. 6

Ans: 1. 9

Solution:

We know that, the number of diagonals in a polygon of n sides is n(n−3) 2 , In hexagon, n = 6 Number of diagonals in a hexagon =

6(6−3) 2 = 6×3 2 = 3 × 3 = 9.

Q37. The number of sides of a regular polygon where each exterior angle has a measure of 45° is.

1. 8

2. 10

3. 4

4. 6

Ans: 1. 8

Solution:

We know that, the sum of exterior angles taken in an order of a polygon is 360° Since, each exterior angle measures 45°, therefore

the number of sides = Sum of exterior angles/ Measure of an exterior angle.

Q38. If the adjacent sides of a parallelogram are equal then parallelogram is a.

1. rectangle

2. trapezium

3. rhombus

4. square

Ans: 3. rhombus

Solution:

We know that, in a parallelogram, opposite sides are equal. But according to the question, adjacent sides are also equal. Thus, the

parallelogram in which all the sides are equal is known as rhombus.

Q39. In a kite, what is false? 

70∘ + ∠B = 180∘

∠B = 180∘ − 70∘ = 110∘

= = 8 360∘

45∘

1. The diagonals are perpendicular to each other.

2. The diagonals bisect each other.

3. Only one pair of opposite angles is equal.

4. All the four sides are equal.

Ans: 4. All the four sides are equal.

Q40. If of a parallelogram ABCD is of 60º, then the measure of the opposite angle is:

1. 60º

2. 120º

3. 30º

4. None of these

Ans: 1. 60º

Solution:

Q41. To construct a unique parallelogram, the minimum number of measurements required is:

1. 2

2. 3

3. 4

4. 5

Ans: 2. 3

Solution:

We know that, in a parallelogram, opposite sides are equal and parallel. Also, opposite angles are equal. So, to construct a

parallelogram uniquely, we require the measure of any two nonparallel sides and the measure of an angle. Hence, the minimum

number of measurements required to draw a unique parallelogram is 3.

Q42. Tick the correct answer in the following?

The interior angle of a regular polygon exceeds its exterior angle by 108°. How many sides does the polygon

have?

1. 16

2. 14

3. 12

4. 10

Ans: 4. 10

Solution:

Each exterior angle of a regular polygon

Each interior angle of a regular polygon

Q43. Diagonals of which of the following quadrilaterals do not bisect it into two congruent triangles?

1. Rhombus

2. Trapezium

3. Square

4. Rectangle

Ans: 2. Trapezium

Solution:

The bases of the trapezium are parallel to each other No sides, angles and diagonals are congruent therefore the diagonals do not

bisect each other in a trapezium.

Q44. For which of the following figures, all angles are equal?

1. Rectangle

2. Kite

∠A ∠C

∠C = ∠A = 60∘

= 360

n

= 180 − 360

n

180 − − 108 = 360

n

360

n

= 180 − 108 = 72 720

n

n = 720 = 10

72

3. Trapezium

4. Rhombus

Ans: 1. Rectangle

Solution:

In a rectangle, all angles are equal, i.e. all equal to 90°.

Q45. What is the number of vertices of a triangle?

1. 1

2. 2

3. 3

4. 4

Ans: 3. 3

Q46. If all the four sides of a parallelogram are equal and the adjacent angles are of 120º and 60º, then the name of

the quadrilateral is:

1. Rectangle

2. Square

3. Rhombus

4. Kite

Ans: 3. Rhombus

Q47. Which of the following can never be the measure of exterior angle of a regular polygon?

1. 22°

2. 36°

3. 45°

4. 30°

Ans: 1. 22°

Solution:

Since, we know that, the sum of measures of exterior angles of a polygon is 360 , i.e. measure of each exterior angle = 360 n ,where

n is the number of sides/ angles.

Thus, measure of each exterior angle will always divide 360 completely.

Hence, 22 can never be the measure of exterior angle of a regular polygon.

Q48.

1. 180°

2. 360°

3. 540°

4. 720°

Ans: 4. 720°

Solution:

Sum of all angles of a n-gon is (n – 2) × 180°.

In hexagon, n = 6, therefore the required sum = (6 – 2) × 180° = 4 × 180° = 720°.

Q49. Which of the following quadrilaterals has a pair of opposite sides parallel?

1. Rhombus

2. Trapezium

3. Kite

4. Rectangle

Ans: 2. Trapezium

Solution:

We know that, a rectangle is a quadrilateral having both pair of opposite sides equal and parallel. Also, all its angles are right

angles.Also, a square is a quadrilateral having all sides equal and both pairs of opposite sides parallel. All its angles are right angles.

And, a parallelogram is a quadrilateral having both pairs of opposite sides equal and parallel. Hence, a parallelogram, square and

° °

°

°

What is the sum of all angles of a hexagon?

rectangle has both pairs of opposite sides equal and parallel. However, a trapezium is a quadrilateral having one pair of opposite sides

parallel.

Q50. Tick the correct answer in the following?

How many diagonals are there in an actagon?

1. 8

2. 16

3. 18

4. 20

Ans: 4. 20

Solution:

For a regular n-sided polygon:

Number of diagonals

For an actagon:

Q51. PQRS is a square. PR and SQ intersect at O. Then is a:

1. Right angle

2. Straight angle

3. Reflex angle

4. Complete angle

Ans: 1. Right angle

Solution:

We know that, the diagonals of a square intersect each other at right angle. Hence, = 90 , i.e, right angle.

Q52. ABCD is a parallelogram as shown. Find x and y.

1. 1, 7

2. 2, 6

3. 3, 5

4. 4, 4

Ans: 3. 3, 5

Solution:

x + y = 8

y + 5 = 10 ⇒ y = 5

x + 5 = 8 ⇒ x = 3.

Q53. Which of the following properties describe a trapezium?

1. A pair of opposite sides is parallel.

2. The diagonals bisect each other.

3. The diagonals are perpendicular to each other.

4. The diagonals are equal.

Ans: 1. A pair of opposite sides is parallel.

=

n(n−3)

2

n = 8

= = 20 8(8−3)

2

40

2

∠POQ

∠POQ °

∴

Solution:

We know that, in a trapezium, a pair of opposite sides are parallel.

Q54. In the trapezium ABCD, the measure of is.

1. 55°

2. 115°

3. 135°

4. 125°

Ans: 4. 125°

Solution:

We know that, in a trapezium, the angles on either sides of base are supplementary angle. In trapezium ABCD,

Q55. Which of the following is not a quadrilateral?

1. Parallelogram

2. Triangle

3. Square

4. Rectangle

Ans: 2. Triangle

Solution:

A quadrilateral is a four-sided polygon but triangle is a three-sided polygon.

Q56. Which of the following can be four interior angles of a quadrilateral?

1. 140 , 40 , 20 , 160

2. 270 , 150 , 30 , 20

3. 40 , 70 , 90 , 60

4. 110 , 40 , 30 , 180

Ans: 1. 140 , 40 , 20 , 160

Solution:

We know that, the sum of interior angles of a quadrilateral is 360 . Thus, the angles in option (a) can be four interior angles of a

quadrilateral as their sum is 360 .

Q57. The sum of the measures of all the three angles of a triangle is:

1. 90º

2. 180º

3. 360º

4. 720º

Ans: 2. 180º

Q58. Tick the correct answer in the following?

Sum of all the interior angles of a hexagon is:

1.

2.

3.

4.

∠D

∴ ∠A + ∠D = 180∘

⇒ 55∘ + ∠D = 180∘

⇒ ∠D = 180∘ − 50∘

⇒ ∠D = 120∘

° ° ° °

° ° ° °

° ° ° °

° ° ° °

° ° ° °

°

°

6 right ∠s

8 right ∠s

9 right ∠s

12 right ∠s

Ans: 2.

Solution:

Sum of all the interior angles of a hexagon is (2n – 4) right angles.

For a hexagon:

Q59. If three angles of a quadrilateral are each equal to 75°, the fourth angle is.

1. 150°

2. 135°

3. 45°

4. 75°

Ans: 2. 135°

Solution:

Given, three angles of quadrilaterals = 75°

Let the fourth angle be x° Then, according to the property, 75° + 75° + 75° + x° = 360°, since sum of the angles of a quadrilateral is

360°.

So, 225° + x° = 360° or x° = 360° – 225° = 135°

Hence, the fourth angle is 135°.

Q60. The angles P, Q, R and S of a quadrilateral are in the ratio 1:3:7:9. Then PQRS is a:

1. parallelogram

2. trapezium with PQ || RS

3. trapezium with QR||PS

4. kite

Ans: 2. trapezium with PQ || RS

Solution:

Let the angles be x, 3x, 7x and 9x, then

⇒ x + 3x + 7x + 9x= 360 ⇒ 20x = 360

⇒ x = 360 20 ⇒ x = 18 Then, the angles P, Q, R and S are 18 , 54 , 126 and 162 respectively Since,

and

The quadrilateral PQRS is a trapezium with PQ || RS

Q61. The angle sum of a convex polygon with number of sides 10 is:

1. 720º

2. 900º

3. 1080º

4. 1440º

Ans: 4. 1440º

Solution:

n = 10

(n – 2) 180º = 1440º.

Q62. The diagonals do not necessarily intersect at right angles in a:

1. Parallelogram.

2. Rectangle.

3. Rhombus.

4. Kite.

Ans: 1. Parallelogram.

8 right ∠s

n = 6

⇒ (2n − 4) Right ∠s = (12 − 4) right ∠s = 8 right ∠s

° °

° ° ° ° ° °

∠P + ∠S = 18∘ + 162∘ = 180∘ ∠Q + ∠R = 54∘ + 126∘ = 180∘

Solution:

The diagonals do not necessarily intersect at right angles in a parallelogram. Only opposite sides, opposite angles are equal and

diagonal bisects each other in parallelogram. If diagonals intersect each other at right angle then it would be square or rhombus.

Q63. The measures of two angles of a quadrilateral are 110º and 100º. The remaining two angles are equal. The

measure of each of the remaining two angles is:

1. 30º

2. 60º

3. 75º

4. 45º

Ans: 3. 75º

Solution:

Required measure

Q64. Which of the following quadrilaterals has two pairs of adjacent sides equal and its diagonals intersect at 90

degrees?

1. Rhombus

2. Rectangle

3. Square

4. Kite

Ans: 4. Kite

Q65. If the diagonals of a quadrilateral are equal and bisect each other, then the quadrilateral is a.

1. rhombus

2. rectangle

3. square

4. parallelogram

Ans: 2. rectangle

Solution:

Since, diagonals are equal and bisect each other, therefore it will be a rectangle.