Class 8th Mathematics MCQ

Q131. Tick the correct answer in the following?

How many diagonals are there in a pentagon?

1. 5

2. 7

3. 6

4. 10

Ans: 1. 5

Solution:

For a pentagon:

n = 5

Number of diagonals

Q132. In an isosceles parallelogram, we have:

1. Pair of parallel sides as equal

2. Pair of non-parallel sides as equal

3. Pair of non-parallel sides as perpendicular

4. None of these

Ans: 2. Pair of non-parallel sides as equal

Solution:

In Euclidean geometry, an isosceles trapezoid (isosceles trapezium in British English) is a convex quadrilateral with a line of symmetry

bisecting one pair of opposite sides. Note that a non-rectangular parallelogram is not an isosceles trapezoid because of the second

condition, or because it has no line of symmetry.

Q133. The diameter of circumcircle of a rectangle is 10 cm and breath of the rectangle is 6 cm. Its length is:

1. 8cm

2. 6cm

3. 5cm

4. None

Ans: 1. 8cm

Q134. The sum of the internal angles of a polygon is 10 right angles. Then the number of sides is:

1. 5

= 180 − ( ) 360

n

180 − ( ) = 135 360

n

⇒ ( 360 ) = 45

n

⇒ n = 8

= = = 5 n(n−3)

2

5(5−3)

2

2. 6

3. 7

4. 8

Ans: 3. 7

Solution:

(n – 2) 180º = 10 × 90º

⇒ n = 7.

Q135. Which of the following figures satisfy the following property? – Has two pairs of congruent adjacent sides.

1. P

2. Q

3. R

4. S

Ans: 3. R

Solution:

We know that, a kite has two pairs of congruent adjacent sides and we can observe that figure R resembles a kite.

Q136. Which of the following is true for the adjacent angles of a parallelogram?

1. They are equal to each other

2. They are complementary angles

3. They are supplementary angles

4. None of these

Ans: 3. They are supplementary angles

Solution:

Parallelogram: A parallelogram is a quadrilateral in which each pair of opposite sides is parallel. The two diagonals bisect each other.

The pair of opposite sides is equal and the pair of opposite angles is equal. Sum of the adjacent angles of a parallelogram is 180º. i,e

supplementary,

Since, the adjacent angles of a parallelogram are supplementary angles.

Q137. A quadrilateral whose all sides, diagonals and angles are equal is a.

1. square

2. trapezium

3. rectangle

4. rhombus

Ans: 1. square

Solution:

These are the properties of a square, i.e. in a square, all sides, diagonals and angles are equal.

Q138. The measure of each exterior angle of a regular polygon of 15 sides is:

1. 30º

2. 45º

3. 60º

4. 24º

Ans: 4. 24º

Q139. Which of the following quadrilaterals has two pairs of adjacent sides equal and diagonals intersecting at right

angles?

1. Square

2. Rhombus

3. Kite

4. Rectangle

Ans: 3. Kite

Solution:

⇒ In given quadrilateral ABCD is a kite

⇒ We know the properties of kite.

⇒ Kite has two pairs of adjacent sides equal.

⇒ AB = AC and BD = CD

⇒ In kite it’s opposite sides are unequal.

⇒ So, If a quadrilateral has exactly two pairs of equal adjacent sides and the unequal opposite sides, then it is called kite.

Q140. If the sides of a triangle are produced in order, What is the sum of the exterior angles so formed?

1. 540º

2. 180º

3. 720º

4. 360º

Ans: 4. 360º

∠A + ∠D = 180∘

Q141. The perimeter of a parallelogram whose parallel sides have lengths equal to 12cm and 7cm is:

1. 19cm

2. 38cm

3. 21cm

4. 42cm

Ans: 2. 38cm

Solution:

Perimeter of parallelogram = 2 (Sum of Parallel sides)

P = 2 (12 + 7)

P = 2 (19)

P = 38cm

Q142. A quadrilateral whose all sides are equal, opposite angles are equal and the diagonals bisect each other at right

angles is a __________.

1. rhombus

2. parallelogram

3. square

4. rectangle

Ans: 1. rhombus

Solution:

We know that, in rhombus, all sides are equal, opposite angles are equal and diagonals bisect each other at right angles.

Q143. Which of the following is a property of a parallelogram?

1. Opposite sides are parallel.

2. The diagonals bisect each other at right angles.

3. The diagonals are perpendicular to each other.

4. All angles are equal.

Ans: 1. Opposite sides are parallel.

Solution:

We, know that, in a parallelogram, opposite sides are parallel.

Q144. ABCD is a rhombus. If then, is:

1. 45º

2. 60º

3. 50º

4. 40º

Ans: 3. 50º

Q145. For which of the following figures, diagonals are equal?

1. Trapezium

2. Rhombus

3. Parallelogram

4. Rectangle

Ans: 4. Rectangle

Solution:

By the property of a rectangle, we know that its diagonals are equal.

Q146. What is the number of sides of a quadrilateral?

1. 1

2. 2

3. 3

4. 4

Ans: 4. 4

∠ACB = 40∘ ∠ADB

Q147. If the two adjacent angles of a parallelogram are equal, then each of its angle is?

1. 70º

2. 80º

3. 90º

4. 100º

Ans: 3. 90º

Q148. The length and breadth of a rectangle are in the ratio 4 : 3. If the diagonal measures 25cm then the perimeter of

the rectangle is:

1. 56cm

2. 60cm

3. 70cm

4. 80cm

Ans: 3. 70cm

Solution:

Let the length AB be 4x and Breadth BC be 3x.

Each angle of a rectangle is a right angle. We have,

From the right

AC2 = AB2 + BC2

⇒ (25) = (4x) + (3x)

⇒ 16x + 9x = 625

⇒ 25x = 625

⇒ x = 25

⇒ x = 5

Therefore, lenght = 4 × 5 = 20cm and breadth = 3 × 5 = 15cm.

Q149. The quadrilateral whose diagonals are perpendicular to each other is:

1. Trapezium

2. Rhombus

3. Parallelogram

4. Rectangle

Ans: 2. Rhombus

Q150. Two adjacent angles of a parallelogram are of equal measure. The measure of each angle of the parallelogram is:

1. 45º

2. 30º

3. 60º

4. 90º

Ans: 4. 90º

Solution:

xº + xº = 180º

⇒ xº = 90º.

Q151. What is the name of a regular polygon of 6 sides?

1. Square

2. Equilateral triangle

3. Regular hexagon

4. Regular octagon

Ans: 3. Regular hexagon

Q152. If an angle of a parallelogram is two-thirds of its adjacent angle, the smallest angle of the parallelogram is:

1. 54º

∴ ∠ABC = 90∘

△ABC :

2 2 2

2 2

2

2

2. 72º

3. 81º

4. 108º

Ans: 2. 72º

Solution:

Let the measure of the angle be xº.

Hence the anlge is 180º.

Its adjacent = (180 – 108º) = 72º.

Therefore, the smallest angle is 72º.

Q153. The two diagonals are not necessarily equal in a:

1. Rectangle.

2. Square.

3. Rhombus.

4. Isosceles trapezium.

Ans: 3. Rhombus.

Solution:

All sides of Rhombus are equal in length but in case of angle it is not necessary to be equal.

If all the angles are equal then it will become a square. That’s why diagonals of rhombus are not necessary to be equal in length.

Q154. 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

Q155. The lengths of the diagonals of a rhombus are 16cm and 12cm. The length of each side of the rhombus is:

1. 8cm

2. 9cm

3. 10cm

4. 12cm

Ans: 3. 10cm

Solution:

From the right we have,

Q156. A parallelogram which has equal diagonals is a:

1. Square

2. Rhombus

3. Rectangle

4. None

Ans: 3. Rectangle

Q157. If the two diagonals of a rhombus are 8cm & 6cm, its area is? 

∴ x + ( 2 × x) = 180

3

⇒ = 180 3x+2x

3

⇒ 5x = 3 × 180

⇒ x = = 180 3×180

5

AO = 1 AC = ( × 16) = 8cm

2

1

2

BO = 1 BD = ( × 12) = 6cm

2

1

2

△AOB,

∴ AB2 = AO2 + BO2

⇒ AB2 = {(8)2 + (6)2}cm2

⇒ AB = √100 = 10cm

1. 28cm

2. 48cm

3. 14cm

4. 24cm

Ans: 4. 24cm

Q158. Which of the following is not true for an exterior angle of a regular polygon with n sides?

1. Each exterior angle

2. Exterior angle = 180 – interior angle

3. n

4. Each exterior angle

Ans: 2. Exterior angle = 180 – interior angle

3. n

4. Each exterior angle

Solution:

4. We know that, (a) and (b) are the formulae to and the measure of each exterior angle, when number of sides and measure of an

interior angle respectively are given and

3. Is the formula to and number of sides of polygon when exterior angle is given. Hence, the formula given in option.

4. Is not true for an exterior angle of a regular polygon with n sides.

Q159. The sum of the measures of the three angles of a triangle is ________.

1. 360º

2. 210º

3. 180º

4. None of these

Ans: 3. 180º

Q160. Tick the correct answer in the following?

In a regular polygon, each interior angle is thrice the exterior angle. The number os sides of the polygon is:

1. 6

2. 8

3. 10

4. 12

Ans: 2. 8

Solution:

For a regular polygon with n sides:

Each exterior angle

Each interior angle

Q161. A diagonal of a rectangle is inclined to one side of the rectangle at 25º. The acute angle between the diagonals is:

1. 25º

2. 50º

3. 40º

4. 55º

Ans: 2. 50º

Q162. What is the number of vertices of a quadrilateral?

1. 1

2. 2

3. 3

4. 4

Ans: 4. 4

Q163. In a parallelogram PQRS, if , then other three angles are:

1. 45 , 135 , 120

2. 60 , 120 , 120

3. 60 , 135 , 135

4. 45 , 135 , 135

Ans: 2. 60 , 120 , 120

Solution:

Given, Since, in a parallelogram, adjacent angles are supplementary,

Also, opposite angles are equal in a parallelogram Therefore,

Hence, other three angles are 60 , 120 , 120 .

Q164. The length and breadth of a rectangle is 4cm and 2cm respectively. Find the perimeter of the rectangle.

1. 8cm

2. 16cm

3. 12cm

4. 6cm

Ans: 3. 12cm

Solution:

Given, length of rectangle is 4cm

Breadth of rectangle = 2cm

By the formula of perimeter of rectangle, we know that;

Perimeter = 2 (Length + Breadth)

P = 2(4 + 2)

P = 2 × 6

P = 12cm.

Q165. What is the maximum exterior angle possible for a regular polygon?

1. 60º

2. 80º

3. 120º

4. 160º

Ans: 3. 120º

Solution:

Since of increasing size of regular polygon ⇒ its exterior angle decreases.

Mass exterior angle is for a regular triangle (equilateral triangle) and = 180 – interior angle

=180º – 60º = 120º

Q166. The angle between the two altitudes of a parallelogram through the same vertex of an obtuse angle of the

parallelogram is 30°. The measure of the obtuse angle is.

1. 100

2. 150

3. 105

4. 120

Ans: 2. 150

Solution:

Let EC and FC be altitudes and

let

so,

So, by property of the parallelogram,

Hence,

Q167. If two adjacent angles of a parallelogram are (5x – 5) and (10x + 35) , then the ratio of these angles is:

1. 1 : 3

2. 2 : 3

3. 1 : 4

4. 1 : 2

Ans: 1. 1 : 3

Solution:

We know that, adjacent angles of a parallelogram are supplementary, i.e., their sum equals 180°

(5𝑥 − 5) + (10x + 35) = 180 .

⇒ 15x+ 30 . = 180 . ⇒ 15x = 180°.

⇒ x = 10 . Thus, the angles are (5 × 10 − 5) and (10 × 10 + 35) i.e.,

45 and 135 . Hence, the required ratio is 45 : 135 i.e., 1:3.

Q168. In the given figure, ABCD and BDCE are parallelograms with common base DC. If BC ⊥ BD, then

1. 60

2. 30

3. 150

4. 120

Ans: 1. 60

Solution:

,

in by angle sum property of a triangle, we have

Q169. The sides of a pentagon are produced in order. Which of the following is the sum of its exterior angles?

1. 540º

2. 180º

3. 720º

4. 360º

Ans: 4. 360º

Solution:

ABCD is a Quadrilateral

To Proof

Each polygon have 360º as it’s exterior angel but it’s Interior angle is depend on it’s sides, so the answer is D.

Q170. The angle sum of a convex polygon with number of sides 8 is:

1. 720º

2. 900º

3. 1080º

4. 1440º

Ans: 3. 1080º

Solution:

n = 8

(n – 2) 180º = 1080º.

Q171. Two adjacent angles of a quadrilateral measure 130º and 40º. The sum of the remaining two angles is:

1. 190º

2. 180º

3. 360º

4. 90º

Ans: 1. 190º

Q172. The measures of the three angles of a quadrilateral are 65º, 75º and 85º. The measure of the fourth angle is:

1. 65º

2. 75º

3. 85º

4. 135º

Ans: 4. 135º

Q173. The closed curve which is also a polygon is:

1.

2.

∵

∠1 + ∠2 + ∠3 + ∠4 = 360∘

∠A + ∠B + ∠C + ∠D = 360∘

∠A + ∠1 = 180∘

∠B + ∠2 = 180∘

∠C + ∠3 = 180∘

∠D + ∠4 = 180∘

∠A + ∠B + ∠C + ∠D + ∠1 + ∠2 + ∠3 + ∠4

= 180∘ + 180∘ + 180∘ + 180∘

= 720∘

360∘ + ∠1 + ∠2 + ∠3 + ∠4 = 720∘

∠1 + ∠2 + ∠3 + ∠4 = 360∘

3.

4.

Ans: 1.

Solution:

is polygon as no two line segments intersect each other.

Q174. ABCD is a rectangle and AC & BD are its diagonals. If AC = 10cm, then BD is:

1. 20cm

2. 10cm

3. 5cm

4. 15cm

Ans: 2. 10cm

Solution:

The diagonals of a rectangle are always equal.

Q175. Tick the correct answer in the following?

How many diagonals are there in a polygon having 12 sides?

1. 12

2. 24

3. 36

4. 54

Ans: 4. 54

Solution:

For an n-sided polygon:

Number of diagonals =

n(n−3)

2

∴ n = 12

⇒ = 54

12(12−3)

2

Q176. The diagonals of a rectangle are 2x + 1 and 3x – 1, respectively. Find the value of x.

1. 2

2. 4

3. 1

4. 3

Ans: 1. 2

Solution:

The diagonals of a rectangle are equal in length.

2x + 1 = 3x – 1

1 + 1 = 3x – 2x

2 = x

Thus, the value of x is 2.

Q177. The sum of angles of a concave quadrilateral is:

1. more than 360

2. less than 360

3. equal to 360

4. twice of 360

Ans: 3. equal to 360

Solution:

We know that, the sum of interior angles of any polygon (convex or concave) having n sides is (n − 2) × 180

The sum of angles of a concave quadrilateral is (4 – 2) × 180 , i.e. 360

Q178. Which of the following quadrilaterals is a regular quadrilateral?

1. Rectangle

2. Square

3. Rhombus

4. Kite

Ans: 2. Square

Solution:

A rhombus is a quadrilateral with all the sides equal and its diagonals bisect each other, but all of its angles are not equal. We already

know that only the parallel sides or the opposite sides of a parallelogram are equal. In a trapezium no side is equal to another. A

rectangle has only its opposite sides as equal. Therefore, square is the only regular quadrilateral. So, the correct answer is “square”.

Note: Do not confuse that rectangle is also a regular quadrilateral. It is not because all the sides are not equal in a rectangle whereas

all the angles are equal and diagonals bisect each other. For a quadrilateral to be regular it should have all the sides equal. So the

rectangle is not. When all the sides are equal in a rectangle, then it can be considered as a square.

Q179. If a quadrilateral has two adjacent sides equal and the other two sides equal, it is called:

1. Square

2. Parallelogram

3. Kite

4. Rectangle

Ans: 3. Kite

Q180. Out of the three equal angles of a quadrilateral, each measures 70º. The measure of the fourth angle is:

1. 90º

2. 140º

3. 150º

4. 70º

Ans: 3. 150º

Solution:

Fourth angle = 360º – (70º + 70º + 70º)

= 150º.

°

°

°

°

°

°

∴ ° °

Q181. A quadrialateral whose opposite sides and all the angles are equal is a.

1. rectangle

2. parallelogram

3. square

4. rhombus

Ans: 1. rectangle

Solution:

We know that, in a rectangle, opposite sides and all the angles are equal.

Q182. Length of one of the diagonals of a rectangle whose sides are 10 cm and 24cm is.

1. 25cm

2. 20cm

3. 26cm

4. 3.5cm

Ans: 3. 26cm

Solution:

In

Using Pythagoras Theorem, We have,

Q183. The perimeter of a parallelogram is 180cm. One side exceeds another by 10cm. The sides of the parallelogram

are:

1. 40cm, 50cm

2. 50cm each

3. 45cm each

4. Cannot be determined

Ans: 1. 40cm, 50cm

Q184. ABCD is a quadrilateral. If AC and BD bisect each other, what is ABCD?

1. A square

2. A parallelogram

3. A rectangle

4. All the above

Ans: 4. All the above

Q185. How many non-overlapping triangles can we make in a n-gon (polygon having n sides), by joining the vertices?

1. n – 1

2. n – 2

3. n – 3

4. n – 4

Ans: 2. n – 2

Solution:

The number of non-overlapping triangles in a n-gon = n – 2, i.e., 2 less than the number of sides.

△BDC = 90∘

BC2 = BD2 + CD2

⇒ BC2 = 102 + 242 = 100 + 576

⇒ BC2 = 676

⇒ BC = √676

⇒ BC = 256cm

Q186. The four angles of a pentagon are 40º, 75º, 125º and 135º. The measure of the fifth angle is:

1. 165º

2. 170º

3. 160º

4. 175º

Ans: 1. 165º

Solution:

n = 5, (n – 2) 180º = (5 – 2) 180º = 540º

Fifth angle

= 540º – (40º + 75º + 125º + 135º)

= 540º – 375º = 165º

Q187. Which of the following statement is true?

1. All the rectangles are squares.

2. All the parallelograms are rhombuses.

3. All the squares are rhombuses.

4. Each parallelogram is a trapezium.

Ans: 3. All the squares are rhombuses.

Q188. How many diagonals does a triangle have?

1. 0

2. 1

3. 2

4. 4

Ans: 1. 0

Q189. A simple closed curve made up of only line segments is called a ________.

1. Polygon

2. Quadrilateral

3. Hexagon

4. None of these

Ans: 1. Polygon

Q190. The number of sides of a regular polygon whose each interior angle is of 135° is:

1. 6

2. 7

3. 8

4. 9

Ans: 3. 8

Solution:

We know that, the measures of each exterior angle of a polygon having n sides is given by

The number of sides,

Q191. Tick the correct answer in the following?

The measure of each exterior angle of a regular polygon is 40º. How many sides does it have?

1. 8

2. 9

3. 6

4. 10

Ans: 2. 9

Solution:

Each exterior angle of a regular n-sided polygon

360∘

n

∴ n = = = = 8 360∘

Exterior angle

360∘

180∘

360∘

45∘

= = 40 160

n

⇒ n = 360 = 9

40

Q192. In the quadrilateral ABCD, the diagonals AC and BD are equal and perpendicular to each other. What type of a

quadrilateral is ABCD?

1. A square

2. A parallelogram

3. A rhombus

4. A trapezium

Ans: 1. A square

Q193. If AB and CD are two parallel sides of a parallelogram, then:

1. AB = CD

2. AB > CD

3. AB < CD

4. None of the above

Ans: 1. AB = CD

Q194. PQRS is a trapezium in which PQ || SR and Then is equal to:

1. 70°

2. 50

3. 65

4. 55

Ans: 1. 70°

Solution:

Since, PQRS is a trapezium and PQ || SR

Q195. How many sides does a regular polygon have if the measure of an exterior angle is 24º ?

1. 6

2. 9

3. 15

4. 12

Ans: 3. 15

Solution:

Number of sides

∠P = 130°,∠Q = 110°. ∠R

°

°

°

∴ ∠Q + ∠R = 180∘

⇒ ∠R = 180∘ − 110∘ = 70∘

= 15 360∘

24∘