Understanding Quadrilaterals Class 8 MCQ Questions with Answers Maths are covered in this Article. Understanding Quadrilaterals Class 8 MCQs Test contains 24 questions. Answers to MCQs on Understanding Quadrilaterals Class 8 Maths are available at the end of the last question. These MCQ have been made for Class 8 students to help check the concept you have learnt from detailed classroom sessions and application of your knowledge.
| Board | CBSE |
| Textbook | Maths (NCERT) |
| Class | Class 8 |
| Chapter | Chapter 3 Understanding Quadrilaterals |
Understanding Quadrilaterals Class 8 MCQ Questions with Answers
1.The three angles of quadrilateral are 87˚ , 163˚ , 25˚ . Find the fourth angle?
(a) 95˚
(b) 85˚
(c) 105˚
Answer
Answer: (b) 85˚
Explanation: Let the measure of the fourth angle be x
According to the angle sum property of Quadrilateral
The sum of all angles of a quadrilateral = 360˚
87˚ + 163˚ + 25˚ + x = 360˚
275˚ + x = 360˚
x = 360˚ – 275˚
x = 85˚
Hence, the fourth angle of the quadrilateral is 85˚
2.If the four angles of quadrilateral are in the ratio of 7 : 5 : 9 : 15, find the measures of each angle?
(a) 80˚ , 87˚ , 150˚ , 75˚
(b) 60˚ , 47˚ , 83˚ , 87˚
(c) 70˚ , 50˚ , 90˚ , 150˚
Answer
Answer: (c) 70˚ , 50˚ , 90˚ , 150˚
Explanation: The ratio of the angles of quadrilateral are = 7 : 5 : 9 : 15
Let, the measures of each angle be 7a , 5a , 9a , 15a
According to Angle sum property of Quadrilateral
The sum of all angles of a quadrilateral = 360˚
7a + 5a + 9a + 15a = 360˚
36a = 360˚
a =360˚/36
a = 10˚
So, 1st angle = 7a = 7 x 10 = 70˚
2nd angle = 5a = 5 x 10 = 50˚
3rd angle = 9a = 9 x 10 = 90˚
4th angle = 15a = 15 x 10 = 150˚
Hence, angles of Quadrilateral are 70˚ , 50˚ , 90˚ and 150˚
3.If the measure of two angles of a quadrilateral are 85˚ and 105˚ and the other two angles are equal, find the measure of each of the equal angles?
(a) 95˚ each
(b) 85˚ each
(c) 100˚ each
Answer
Answer: (b) 85˚ each
Explanation: Let the measure of each of the equal angle be x
According to Angle sum property of Quadrilateral
The sum of all angles of a quadrilateral = 360˚
85˚ + 105˚ + x + x = 360˚
190˚ + 2x = 360˚
2x = 170˚
x =170˚/2
x = 85˚
Hence, the measure of equal angles is 85˚
4.If three angles of quadrilateral are equal and the measure of the fourth angle is 132˚ , find the measure of each of the three equal angle?
(a) 91˚ each
(b) 86˚ each
(c) 76˚ each
Answer
Answer: (c) 76˚ each
Explanation: Let the measure of each of the equal angle be x
According to Angle sum property of Quadrilateral
The sum of all angles of a quadrilateral = 360˚
132˚ + x + x + x = 360˚
132˚ + 3x = 360˚
3x = 360˚ – 132˚
3x = 228˚
x =228˚/3
x = 76˚
Hence, the measure of each equal angle is 76˚
5.Can a rectangle be a square?
(a) Yes
(b) No
Answer
Answer: (b) No
6. Can a square be a rhombus?
(a) Yes
(b) No
Answer
Answer: (a) Yes
7. Can a parallelogram be a kite?
(a) Yes
(b) No
Answer
Answer: (b) No
Understanding Quadrilaterals Class 8 MCQ Questions with Answers
8. Can a rhombus be a kite?
(a) Yes
(b) No
Answer
Answer: (a) Yes
9. Can a trapezium be a parallelogram?
(a) Yes
(b) No
Answer
Answer: (b) No
10. Can a kite be a rhombus?
(a) Yes
(b) No
Answer
Answer: (b) No
11.If two adjacent angles of a parallelogram are in the ratio of 3 : 2 , find the measure of both the angles?
(a) 108˚ and 72˚
(b) 96˚ and 84˚
(c) 116˚ and 64˚
Answer
Answer: (a) 108˚ and 72˚
Explanation: Let the measure of the adjacent angle be 3x and 2x
Measure of one angle = 3x
Measure of the other angle = 2x
As we know that,
Sum of adjacent angle of a parallelogram = 180˚
3x + 2x = 180˚
5x = 180˚
x =180˚/5
x = 36˚
Measure of one angle = 3x = ( 3 x 36˚ ) = 108˚
Measure of the other angle = 2x = ( 2 x 36˚ ) = 72˚
12.If two sides of square are ( 13 + 16x ) cm and ( 14x + 73 ) cm , find the value of x?
(a) 29
(b) 30
(c) 31
Answer
Answer: (b) 30
Explanation: As we know,
All sides of square are equal
This means that
( 13 + 16x ) = ( 14x + 73 )
16x – 14x = 73 – 13
2x = 60
x = 30
Hence, the value of x is 30
13.If two sides of parallelogram are in ratio 6 : 2 and its perimeter is 80 cm , find the length of its sides ?
(a) 30 cm and 10 cm
(b) 28 cm and 9 cm
(c) 32 cm and 12 cm
Answer
Answer: (a) 30 cm and 10 cm
Explanation: Let the measure of the two sides of the parallelogram be 6x cm and 2x cm
As we know that,
Perimeter of Parallelogram = 2 ( Measure of Side 1 + Measure of Side 2 )
Perimeter of Parallelogram = 2 ( 6x + 2x ) cm
= 2 ( 8x ) cm
= 16x cm
Given, Perimeter = 80 cm
therefore,
16x = 80
x =80/16
x = 5
Ist side = 6x cm = ( 6 x 5 ) cm = 30 cm
IInd side = 2x cm = ( 2 x 5 ) cm = 10 cm
Hence, the measure of the two sides are 30 cm and 10 cm respectively.
14.The sum of two opposite angles of a parallelogram is 200˚ , find the measure of both the angles ?
(a) 90˚ each
(b) 100˚ each
(c) 95˚ each
Answer
Answer: (b) 100˚ each
Explanation: We know that,
Opposite angles of parallelograms are equal
Let the measure of both angles be x
Given,
Sum of opposite angles of parallelogram = 200˚
x + x = 200˚
2x = 200˚
x =200˚/2
x = 100 ˚
Hence, the measure of each of the opposite angles is 100 ˚
Understanding Quadrilaterals Class 8 MCQ Questions with Answers
15.Two adjacent angles of a parallelogram are ( 17x + 25 )˚ and ( 40 + 6x )˚. Find the value of x ?
(a) 5
(b) 3
(c) 8
Answer
Answer: (a) 5
Explanation: We know that the Sum of adjacent angles of a parallelogram = 180 ˚
( 17x + 25 )˚ + ( 40 + 6x )˚ = 180 ˚
( 17x + 6x ) + ( 25 + 40 ) = 180
23x + 65 = 180
23x = 180 – 65
23x = 115
x =115/23
x = 5
16. If a polygon has 12 sides , find the measure of its exterior angle?
(a) 30˚
(b) 45˚
(c) 24˚
Answer
Answer: (a) 30˚
Explanation: Given,
Number of sides of Polygon = 12
As we know that,
Exterior angle of a Polygon = 360˚/n
Where,
n = Number of sides of Polygon
Exterior angle of a Polygon = 360˚/12
Exterior angle of a Polygon = 30˚
17. Is it possible to have a polygon each of whose exterior angle is 45˚ ?
(a) Yes
(b) No
Answer
Answer: (a) Yes
Explanation: Let us assume that number of sides of the polygon are “n”
We know that,
Exterior angle of a polygon = 360˚/n ——— Equation 1
Where,
n = number of sides of polygon
Given,
Exterior angle of a polygon = 45˚ ——— Equation 2
From equation 1 and 2 we get,
45˚ = 360˚/n
n = 360˚/45˚
n = 8˚
Since, the number of sides is 8˚ ,which is a whole number, It is possible to have a regular pentagon the measure of whose exterior angle is 45˚
18.If a polygon has 15 sides , find the measure of its interior angle ?
(a) 136˚
(b) 126˚
(c) 156˚
Answer
Answer: (c) 156˚
Explanation: Given,
Number of sides of Polygon = 15
Interior Angle of a Polygon = 180˚ – Exterior angle
We know that
Exterior angle of a Polygon = 360˚/n
Where,
n = Number of sides of Polygon
Exterior angle of a Polygon = 360˚/15
Exterior angle of a Polygon = 24˚
Since,
Interior Angle of a Polygon = 180˚ – 24˚
Interior Angle of a Polygon = 156˚
19.If each exterior angle of a polygon is 30˚ , find the number of sides of the Polygon ?
(a) 12
(b) 8
(c) 4
Answer
Answer: (a) 12
Explanation: Given,
Exterior angle of a Polygon = 30˚
Exterior angle of a Polygon = 360˚/n
Where,
n = number of sides
Since,
30˚ = 360˚/n
n = 360˚/30˚
n = 12
Hence, the given Polygon has 12 sides.
20.If each interior angle of a polygon is 120˚ , find the number of sides of the Polygon ?
(a) 6
(b) 5
(c) 8
Answer
Answer: (a) 6
Explanation: Given,
Interior Angle of a Polygon = 120˚
As we know that,
Interior Angle of a Polygon = 180˚ – Exterior angle
Exterior angle of a Polygon = 180˚ – Interior Angle of a Polygon
Exterior angle of a Polygon = 180˚ – 120˚
Exterior angle of a Polygon = 60˚ —————- Equation 1
or we know that,
Exterior angle of a Polygon = 360˚/n —————- Equation 2
Where,
n = number of sides in a given polygon
From equation 1 and 2 we get,
60˚ = 360˚/n
n = 360˚/60˚
n = 6
Hence, the Polygon has 6 sides
21.If a polygon has 35 diagonals , find the number of sides which the polygon has ?
(a) 7
(b) 10
(c) 14
Answer
Answer: (b) 10
Explanation: Number of diagonals in a polygon of ‘n’ sides = [n(n−3)]/2
Where,
n = number of sides of polygon
Given:
Number of diagonals in a polygon = 35
in other words
35 = [n(n−3)]/2
70 = n( n – 3 )
70 = n2 – 3n
n2 – 3n – 70 = 0
n2 – 10n + 7n – 70 = 0
n( n – 10 ) + 7( n – 10 ) = 0
( n – 10 ) ( n + 7 ) = 0
If
n – 10 = 0
n = 10
or n + 7 = 0
n = -7
which is not possible because sides of polygons can’t be negative
Hence, number of sides of polygon which has 35 diagonals = 10
Understanding Quadrilaterals Class 8 MCQ Questions with Answers
22.Dodecagon has _____ diagonals.
(a) 56
(b) 53
(c) 54
Answer
Answer: (c) 54
Explanation: Number of diagonals in a polygon which has “n” number of sides = [n(n−3)]/2
Where,
n = number of sides of polygon
Number of sides in a Dodecagon = 12
Number of diagonals in a Dodecagon = [12(12−3)]/2
= (12×9)/2
= 108/2
Number of diagonals in a Dodecagon = 54
23.Pentadecagon has _____ diagonals.
(a) 92
(b) 89
(c) 90
Answer
Answer: (c) 90
Explanation: Number of diagonals in a polygon which has “n” number of sides = [n(n−3)]/2
Where,
n = number of sides of polygon
Number of sides in a Pentadecagon = 15
Number of diagonals in a Pentadecagon = [15(15−3)]/2
= (15×12)/2
= 180/2
Number of diagonals in a Pentadecagon = 90
24.If a polygon has 21 sides. The sum of all interior angles of a polygon would be ?
(a) 1800˚
(b) 3420˚
(c) 1980˚
Answer
Answer: (b) 3420˚
Explanation: Given,
Number of sides in the given polygon = 21
As we know that,
Sum of all interior angles of a polygon = ( 2n – 4 ) 90˚
Where,
n = Number of sides in the given polygon
So,
Sum of all interior angles of a polygon = ( 2 x 21 – 4 ) 90˚
Sum of all interior angles of a polygon = ( 42 – 4 ) 90˚
Sum of all interior angles of a polygon = 38 x 90˚
Sum of all interior angles of a polygon = 3420˚
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Frequently Asked Questions on Understanding Quadrilaterals Class 8 MCQ Questions
1. Are these MCQs on Understanding Quadrilaterals Class 8 are based on 2021-22 CBSE Syllabus?
Yes. There are 24 MCQ’s on this Chapter in this blog.
2. Are you giving all the chapters of Maths Class 8 MCQs with Answers which are given in CBSE syllabus for 2021-22 ?
Yes, we are providing all the chapters of Maths Class 8 MCQs with Answers.