Class 8th Mathematics MCQ

Q66. In a parallelogram ABCD, if AB = 2x + 5, CD = y + 1, AD = y + 5 and BC = 3x – 4 then ratio of AB : BC:

1. 31 : 35

2. 71 : 21

3. 12 : 11

4. 4 : 7

Ans: 1. 31 : 35

Q67. ABCD is a square E, F, G, H are the mid-mid-points of the four sides. Then the figure EFGH is:

1. Trapezium

2. Square

3. Rectangle

4. Parallelogram

Ans: 2. Square

Q68. How many diagonals does a quadrilateral have?

1. 1

2. 2

3. 3

4. 4

Ans: 2. 2

= = 75 360 ∘ ∘−(110∘+100∘)

2

Q69. State the name of a regular polygon of 6 sides.

1. Pentagon

2. Hexagon

3. Heptagon

4. None of these

Ans: 2. Hexagon

Q70. Which one has all the properties of a kite and a parallelogram?

1. Trapezium

2. Rhombus

3. Rectangle

4. Parallelogram

Ans: 2. Rhombus

Solution:

In a kite Two pairs of equal sides. Diagonals bisect at 90°. One pair of opposite angles are equal. In a parallelogram Opposite sides are

equal. Opposite angles are equal. Diagonals bisect each other. So, from the given options, all these properties are satisfied by

rhombus.

Q71. AB and CD are diameters. Then ACBD is:

1. Trapezium

2. Square

3. Rectangle

4. Isosceles trapezium

Ans: 3. Rectangle

Q72. Which of the following statement is false?

1. All the four angles of a rhombus are equal.

2. The diagonals of a rhombus bisect each other at right angles.

3. A rectangle is a parallelogram.

4. All squares are rectangles.

Ans: 1. All the four angles of a rhombus are equal.

Q73. Which of the following figures satisfy the following property? – Only one pair of sides are parallel.

1. P

2. Q

3. R

4. S

Ans: 1. P

Solution:

We know that, in a trapezium, only one pair of sides are parallel and we can observe that figure P resembles a trapezium.

Q74. Which of the following is a formula to find the sum of interior angles of a quadrilateral of n-sides?

1.

2.

3.

4.

Ans: 4.

Solution:

The sum of the interior angles, in degrees, of a regular polygon is given by the formula (n – 2) × 180, where n is the number of sides.

The problem concerns a polygon with twelve sides, so we will let n = 12. The sum of the interior angles in this polygon would be

180(12 – 2) = 180(10) = 1800.

Q75. Which of the following statement is false?

1. All the four sides of a parallelogram are equal.

2. The opposite angles of a parallelogram are equal.

3. The diagonals of a parallelogram bisect each other.

4. All the four sides of a rhombus are equal.

Ans: 1. All the four sides of a parallelogram are equal.

Q76. The angles of a quadrilateral are in ratio 1 : 2 : 3 : 4. Which angle has the largest measure?

1. 98º

2. 36º

3. 120º

4. 144º

Ans: 4. 144º

Solution:

Suppose, ABCD is a quadrilateral.

Let angle A is x

Then,

x + 2x + 3x + 4x = 360º [Angle sum property of quadrilateral] 10x = 360º

x = 36º

Hence, the greatest angle is 4x = 4 × 36 = 144º

n × 180∘

2(

n+1 ) × 180∘

2

( n−1 ) × 180∘

2

(n– 2) × 180∘

(n– 2) × 180∘

Q77. If PQ and RS are two perpendicular diameters of a circle, then PQRS is a:

1. Rectangle

2. Square

3. Trapezium

4. Rhombus but not square

Ans: 2. Square

Q78. What is the number of sides of a triangle?

1. 1

2. 2

3. 3

4. 4

Ans: 3. 3

Q79. To construct a unique rectangle, the minimum number of measurements required is:

1. 4

2. 3

3. 2

4. 1

Ans: 3. 2

Solution:

Since, in a rectangle, opposite sides are equal and parallel, so we need the measurement of only two adjacent sides, i.e. length and

breadth.

Q80. The four angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. The measure of its smallest angle is:

1. 120º

2. 36º

3. 18º

4. 10º

Ans: 2. 36º

Solution:

Sum of the ratios = 1 + 2 + 3 + 4 = 10

Smallest angle

Q81. Which of the following is not a regular polygon?

1. Rectangle

2. Regular hexagon

3. Square

4. Equilateral triangle

Ans: 1. Rectangle

Solution:

A regular polygon is both equiangular and equilateral. But all four sides of a rectangle are not equal, thus it is not a regular polygon.

Q82. The diagonal of a rectangle is 10cm and its breadth is 6cm. What is its length?

1. 6cm.

2. 5cm.

3. 8cm.

4. 4cm.

Ans: 3. 8cm.

Q83. Choose the correct statement:

1. Every quadrilateral is either a trapezium or a parallelogram or a kite.

2. The diagonals of a rectangle are perpendicular to each other.

∴ = 1 × 360∘ = 36∘

10

3. The diagonals of a parallelogram are equal.

4. If the diagonals of a quadrilateral intersect at right angles, it is not necessary a rhombus.

Ans: 4. If the diagonals of a quadrilateral intersect at right angles, it is not necessary a rhombus.

Q84. Which of the following statement is true?

1. All the rhombuses are squares.

2. Each square is a parallelogram.

3. Each parallelogram is a square.

4. Each trapezium is a parallelogram.

Ans: 2. Each square is a parallelogram.

Q85. Which of the following is an equiangular and equilateral polygon?

1. Square

2. Rectangle

3. Rhombus

4. Right triangle

Ans: 1. Square

Solution:

In a square, all the sides and all the angles are equal. Hence, square is an equiangular and equilateral polygon.

Q86. How many diagonals does a rectangle have?

1. 2

2. 1

3. 0

4. None of these

Ans: 1. 2

Q87. The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. The smallest angle is.

1. 72

2. 144

3. 36

4. 18

Ans: 3. 36

Solution:

Let the angles of the given quadrilaterals be x , 2x , 3x and 4x

x + 2x + 3x + 4x = 360

⇒ 10x = 360

⇒ x = 360 10 = 36

Hence, the smallest angle = 36 .

Q88. How many sides does a-regular polygon have if each of its interior angles is 165º?

1. 12

2. 24

3. 9

4. 6

Ans: 2. 24

Solution:

Exterior angle = 180º – 165º = 15º

Number of sides

Q89. Which one of the following is a regular quadrilateral?

1. Rectangle

2. Kite

°

°

°

°

°

° ° ° °

∴ ° ° ° ° °

°

° ° °

°

∴ = 24 360∘

15∘

3. Square

4. Trapezium

Ans: 3. Square

Solution:

A square has all its sides equal and angles equal to 90 degrees.

Q90. Tick the correct answer in the following?

Each interior angle of a polygon is 108°. How many sides does it have?

1. 8

2. 6

3. 5

4. 7

Ans: 3. 5

Solution:

Each interior angle for a regular n-sided polygon

Q91. What is the name of a regular polygon of 3 sides?

1. Equilateral triangle

2. Square

3. Regular hexagon

4. Regular octagon

Ans: 1. Equilateral triangle

Q92. Which of the parallelograms has all sides equal and diagonals bisect each other at right angle?

1. Square

2. Rectangle

3. Rhombus

4. Trapezium

Ans: 3. Rhombus

Solution:

A square is a parallelogram in which adjacent sides are equal and one angle is of 90º. In a parallelogram, opposite sides are equal,

opposite angles are equal and diagonals bisect each other. In a rhombus diagonal intersect at right angles.

Q93. The number of sides of a regular polygon, whose each exterior angle has a measure of 45º, is:

1. 4

2. 6

3. 8

4. 10

Ans: 3. 8

Solution:

Number of sides

Q94. ABCD is a parallelogram. If angle A is equal to 45º, then find the measure of its adjacent angle.

1. 115º

2. 180º

3. 135º

4. 120º

Ans: 3. 135º

Solution:

= 180 − ( ) 360

n

180 − ( ) = 108 360

n

⇒ ( 360 ) = 72

n

⇒ n = 360 = 5

n

= = 8. 360∘

45∘

The adjacent angles of a parallelogram sums up to 180º.

Thus,

45º + x = 180º

x = 180º – 45º

x = 135º

Q95. Find the perimeter of a rectangle whose two adjacent sides are:

5x + 2xy – 13; 2x – 6xy + 11

1. 14x – 8xy – 4

2. x – 8xy – 3

3. 4x – 8xy – 3

4. 12x – 8xy – 4

Ans: 1. 14x – 8xy – 4

Solution:

Perimeter of a rectangle is 2(L +B)

Given, two adjacent side are 5x + 2xy -13, 2x – 6xy + 11

Therefore,

2(L +B)

= 2(5x + 2xy -13, 2x – 6xy + 11)

= 2(7x – 4xy -2)

= 14x – 8xy – 4

Q96. ABCD is a rectangle. Its diagonals meet at O.

OA = 2x – 1, OD = 3x – 2. Find x

1. 1

2. 2

3. 3

4. -1

Ans: 1. 1

Solution:

3x – 2 = 2x – 1 ⇒ x = 1.

Q97. The sum of the angles of a quadrilateral is:

1. 180º

2. 270º

3. 360º

4. Depends on the quadrilateral

Ans: 3. 360º

Q98. Tick the correct answer in the following?

How many diagonals are there in a hexagon?

1. 6

2. 8

3. 9

4. 10

Ans: 3. 9

Solution:

Number of diagonals in an n-sided polygon

2 2

2

2

2

2

2

2 2

2 2

2

2

=

n(n−3)

2

Q99. Two adjacent sides of a rectangle are equal. The name of the quadrilateral is:

1. Square

2. Kite

3. Rhombus

4. None of these

Ans: 1. Square

Q100. Which of the following statement is false?

1. All the rectangles are parallelograms.

2. All the squares are rectangles.

3. All the parallelograms are rectangles.

4. All the rhombuses are parallelograms.

Ans: 3. All the parallelograms are rectangles.

Q101. A quadrilateral has three acute angles. If each measures 80°, then the measure of the fourth angle is.

1. 150°

2. 120°

3. 105°

4. 140°

Ans: 2. 120°

Solution:

Let the fourth angle be x.

Q102. The diagonals do not necessarily bisect the interior angles at the vertices in a:

1. Rectangle.

2. Square.

3. Rhombus.

4. All of these.

Ans: 1. Rectangle.

Solution:

In rectangle, only opposite sides are equal which makes diagonals are not to be perpendicular to each other. As diagonals are not

perpendicular to each other, they will not bisect the interior angles.

Q103. Tick the correct answer in the following?

A polygon has 27 diagonals. How many sides does it have?

1. 7

2. 8

3. 9

4. 12

Ans: 3. 9

Solution:

n = 6

∴ =

n(n−3)

2

6(6−3

2

= = 9 18

9

80∘ + 80∘ + 80∘ x∘ = 360∘

⇒ 240∘ + x = 360∘

⇒ x = 360∘ − 240∘

⇒ x = 120∘

= 27

n(n−3)

2

⇒ (n − 3) = 54

⇒ n2 − 3n − 54 = 0

⇒ n2 − 9n + 6n − 54 = 0

⇒ n(n − 9) + 6(n − 9) = 0

Number of sides cannot be negative.

Q104. If angles P, Q, R and S of the quadrilateral PQRS, taken in order, are in the ratio 3:7:6:4 then PQRS is a:

1. Rhombus

2. Parallelogram

3. Kite

4. Trapezium

Ans: 4. Trapezium

Q105. If two adjacent angles of a parallelogram are in the ratio 2 : 3, then the measure of angles are:

1. 72 , 108

2. 36 , 54

3. 80 , 120

4. 96 , 144

Ans: 1. 72 , 108

Solution:

Let the angles be 2x and 3x. Then, 2x + 3x = 180 [adjacent angles of a parallelogram are supplementary]

⇒ 5x = 180

⇒ x = 36

Hence, the measures of angles are 2x = 2 × 36 = 72 and 3x = 3 × 36 = 108

Q106. If the length of a side of a rhombus is 6cm, then the perimeter of the rhombus is:

1. 6cm

2. 12cm

3. 24cm

4. 3cm

Ans: 3. 24cm

Solution:

Perimeter = 4 side

= 4 × 6 = 24cm

Q107. Two adjacent angles of a parallelogram are (2x + 25)° and (3x – 5)°. The value of x is:

1. 28

2. 32

3. 36

4. 42

Ans: 2. 32

Solution:

(2x + 25) + (3x – 5) = 180

⇒ 2x + 25 + 3x – 5 = 180

⇒ 5x = 180 – 20

⇒ 5x = 160

⇒ x = 32

Q108. In the figure, BEST is a rhombus, Then the value of y – x is:

1. 40

2. 50

3. 20

4. 10

⇒ n = −6 or n = 9

∴ n = 9

° °

° °

° °

° °

° °

°

°

°

° ° ° °

∴

°

°

°

°

Ans: 1. 40

Given, a rhombus BEST 𝑇𝑆|| 𝐵𝐸 and 𝐵𝑆 is transversal.

Also, y =

In

Q109. If two adjacent angles of a parallelogram are in the ratio 3 : 2, then the measure of the angles are:

1. 100º, 80º

2. 72º, 36º

3. 108º, 72º

4. 144º, 36º

Ans: 3. 108º, 72º

Q110. What is the maximum number of obtuse angles that a quadrilateral can have?

1. 1

2. 2

3. 3

4. 4

Ans: 3. 3

Solution:

We know that, the sum of all the angles of a quadrilateral is 360°. Also, an obtuse angle is more than 90° and less than 180°.

Q111. What is the minimum interior angle possible for a regular polygon?

1. 60º

2. 80º

3. 120º

4. 160º

Ans: 1. 60º

Solution:

Since on increasing the size of regular polygon ⇒ its angle increase.

Minimum interior angle for regular triangle. i.e. equilateral triangle and Minimum interior angle = 60º

Q112. Find the perimeter of the rectangle ABCD.

1. 6cm

2. 12cm

3. 3cm

4. 24cm

Ans: 2. 12cm

Solution:

°

Solution:

∴ ∠SBE = ∠TSB = 40∘

90∘

△TSO,∠STO + ∠TOS = ∠SOE

⇒ x + 40∘ + 90∘

⇒ x = 50∘

⇒ y − x = 90∘ − 50∘ = 40∘

Perimeter = 2 (4 + 2)cm = 12cm.

Q113. Which of the following statement is false?

1. A square is a rectangle whose adjacent sides are equal.

2. A square is a rhombus whose one angle is a right angle.

3. The diagonals of a square bisect each other at right angles.

4. The diagonals of a square do not divide the whole square into four equal parts.

Ans: 4. The diagonals of a square do not divide the whole square into four equal parts.

Q114. How many sides does a regular polygon has if each of it’s interior angle is 120º?

1. Eight

2. Seven

3. Six

4. Five

Ans: 3. Six

Solution:

Let assume polygon is regular polygon.

The measure of an interior angle, A, of a regular polygon of n sides is given by:

The regular polygon has 6 equal sides and is called a hexagon.

Q115. The sum of all exterior angles of a triangle is.

1. 180°

2. 360°

3. 540°

4. 720°

Ans: 2. 360°

Solution:

We know that the sum of exterior angles, taken in order of any polygon is 360° and triangle is also a polygon. Hence, the sum of all

exterior angles of a triangle is 360°.

Q116. Which of the quadrilaterals has all angles as right angles, opposite sides equal and diagonals bisect-each other?

1. Rectangle

2. Rhombus

3. Square

4. None of these

Ans: 1. Rectangle

Solution:

A rectangle is a quadrilateral in which all angles are right angles. A rectangle is a parallelogram, so its opposite sides are equal. The

diagonals of a rectangle are equal and bisect each other.

Q117. How many diagonals does a regular hexagon have?

1. 2

2. 0

3. 4

4. 9

Ans: 4. 9

Q118. Which of the following figures do not satisfy any of the following properties? 

A =

(n−2)180∘

n

⇒ 120∘ = × 180∘. (n−2)

n

⇒ = n − 2 120∘n

180∘

⇒ = n − 2 2

n

⇒ 2n = 3n − 6

⇒ n = 6

∴

All sides are equal.

All angles are right angles.

Opposite sides are parallel.

1. P

2. Q

3. R

4. S

Ans: 1. P

Solution:

On observing the above figures, we conclude that the figure P does not satisfy any of the given properties.

Q119. The measure of each exterior angle of a regular polygon of 9 sides is:

1. 30º

2. 40º

3. 60º

4. 45º

Ans: 2. 40º

Solution:

Required measure

Q120. The angle sum of a convex polygon with number of sides n is:

1. (n – 2) 180º

2. (n + 2) 180º

3. (2n – 4) 180º

4. (2n + 4) 180º

= 360 = 40∘ ∘

9

Ans: 1. (n – 2) 180º

Q121. How many diagonals does a convex quadrilateral has?

1. One

2. Two

3. Three

4. Four

Ans: 2. Two

Solution:

A convex quadrilateral is a four sided figure with interior angles of less than 180 degrees each and both of its diagonals contained

within the shape. It has got two Diagonals.

Q122. The diagonals of a kite:

1. Does not bisect each other

2. None of the above

3. Are perpendicular to each other

4. Bisects each other

Ans: 3. Are perpendicular to each other

Solution:

The diagonals of a kite are perpendicular to each other. They intersect at 90 degrees but does not bisect.

Q123. Tick the correct answer in the following?

Each interior angle of a regular decagon is:

1. 60º

2. 120º

3. 144º

4. 180º

Ans: 3. 144º

Solution:

Each interior angle of a regular decagon

Q124. The measures of each of the four angles of a quadrilateral are equal. Find the measure of each angle.

1. 45º

2. 30º

3. 60º

4. 90º

Ans: 4. 90º

Solution:

Measure of each angle

Q125. A _______ is both ‘equiangular’ and ‘equilateral’.

1. Regular polygon

2. Triangle

3. Quadrilateral

4. None of these

Ans: 1. Regular polygon

Q126. The angle sum of a convex polygon with number of sides 7 is:

1. 900º

2. 1080º

3. 1440º

4. 720º

= 180 − 360 = 180 − 36 = 144∘

10

= 360 = 90∘ ∘

4

Ans: 1. 900º

Solution:

n = 7

(n – 2) 180º = 900º

Q127. In the quadrilateral ABCD, the diagonals AC and BD are equal and perpendicular to each other. Then ABCD is a:

1. Square

2. Rhombus

3. Parallelogram

4. Trapezium

Ans: 1. Square

Q128. Which of the following figures satisfy the following properties?

All sides are congruent.

All angles are right angles.

Opposite sides are parallel.

1. P

2. Q

3. R

4. S

Ans: 3. R

Solution:

We know that all the properties mentioned above are related to square and we can observe that figure R resembles a square.

Q129. What is the sum of all the angles of a pentagon?

1. 180°

2. 360°

3. 540°

4. 720°

Ans: 3. 540°

Solution:

We know that, the sum of angles of a polygon is (n – 2) × 180°, where n is the number of sides of the polygon.

In pentagon, n = 5 Sum of the angles = (n – 2) × 180° = (5 – 2) × 180° = 3 × 180° = 540°.

Q130. Tick the correct answer in the following?

Each interior angle of a polygon is 135°. How many sides does it have?

1. 8

2. 7

3. 6

4. 10

Ans: 1. 8

Solution:

Each interior angle for a regular polygon withn-sided