Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral

Quadrilateral Exercise 27A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Two angles of a quadrilateral are 89° and 113°. If the other two angles are equal; find the equal angles.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 1

Question 2.
Two angles of a quadrilateral are 68° and 76°. If the other two angles are in the ratio 5 : 7; find the measure of each of them.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 2

Question 3.
Angles of a quadrilateral are (4x)°, 5(x+2)°, (7x-20)° and 6(x+3)°. Find
(i) the value of x.
(ii) each angle of the quadrilateral.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 3

Question 4.
Use the information given in the following figure to find :
(i) x
(ii) ∠B and ∠C
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A Q4
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 4

Question 5.
In quadrilateral ABCD, side AB is parallel to side DC. If ∠A : ∠D = 1 : 2 and ∠C : ∠B = 4:5
(i) Calculate each angle of the quadrilateral.
(ii) Assign a special name to quadrilateral ABCD.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 5

Question 6.
From the following figure find ;
(i) x,
(ii) ∠ABC,
(iii) ∠ACD.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 6

Question 7.
Given : In quadrilateral ABCD ; ∠C = 64°, ∠D = ∠C – 8° ;
∠A = 5(a+2)° and ∠B = 2(2a+7)°.
Calculate ∠A.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 7

Question 8.
In the given figure :
∠b = 2a + 15
and ∠c = 3a+5; find the values of b and c.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A Q8
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 8

Question 9.
Three angles of a quadrilateral are equal. If the fourth angle is 69°; find the measure of equal angles.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 9

Question 10.
In quadrilateral PQRS, ∠P : ∠Q : ∠R : ∠S = 3 : 4 : 6 : 7.
Calculate each angle of the quadrilateral and then prove that PQ and SR are parallel to each other. Is PS also parallel to QR ?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 10

Question 11.
Use the information given in the following figure to find the value of x.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 11

Question 12.
The following figure shows a quadrilateral in which sides AB and DC are parallel.
If ∠A : ∠D = 4 : 5, ∠B = (3x – 15)° and ∠C = (4x + 20)°, find each angle of the quadrilateral ABCD.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A Q12
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27A 12

Quadrilateral Exercise 27B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
In a trapezium ABCD, side AB is parallel to side DC. If ∠A = 78° and ∠C = 120°, find angles B and D.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 13

Question 2.
In a trapezium ABCD, side AB is parallel to side DC. If ∠A = x° and ∠D = (3x – 20)°; find the value of x.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 14

Question 3.
The angles A, B, C and D of a trapezium ABCD are in the ratio 3 : 4 : 5 : 6.
Le. ∠A : ∠B : ∠C : ∠D = 3:4: 5 : 6. Find all the angles of the trapezium. Also, name the two sides of this trapezium which are parallel to each other. Give reason for your answer
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 15

Question 4.
In an isosceles trapezium one pair of opposite sides are ….. to each Other and the other pair of opposite sides are ….. to each other.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 16

Question 5.
Two diagonals of an isosceles trapezium are x cm and (3x – 8) cm. Find the value of x.
Solution:
<Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 17

Question 6.
Angle A of an isosceles trapezium is 115° ; find the angles B, C and D.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 18

Question 7.
Two opposite angles of a parallelogram are 100° each. Find each of the other two opposite angles.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 19

Question 8.
Two adjacent angles of a parallelogram are 70° and 110° respectively. Find the other two angles of it.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 20

Question 9.
The angles A, B, C and D of a quadrilateral are in the ratio 2:3: 2 : 3. Show this quadrilateral is a parallelogram.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 21
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 22

Question 10.
In a parallelogram ABCD, its diagonals AC and BD intersect each other at point O.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B Q10
If AC = 12 cm and BD = 9 cm ; find; lengths of OA and OD.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 23

Question 11.
In parallelogram ABCD, its diagonals intersect at point O. If OA = 6 cm and OB = 7.5 cm, find the length of AC and BD.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B Q11
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 24

Question 12.
In parallelogram ABCD, ∠A = 90°
(i) What is the measure of angle B.
(ii) Write the special name of the paralleogram.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 25

Question 13.
One diagnol of a rectangle is 18 cm. What is the length of its other diagnol?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 26

Question 14.
Each angle of a quadrilateral is x + 5°. Find :
(i) the value of x
(ii) each angle of the quadrilateral.
Give the special name of the quadrilateral taken.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B Q14
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 27

Question 15.
If three angles of a quadrilateral are 90° each, show that the given quadrilateral is a rectangle.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 28

Question 16.
The diagnols of a rhombus are 6 .cm and 8 cm. State the angle at which these diagnols intersect.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 29

Question 17.
Write, giving reason, the name of the figure drawn alongside. Under what condition will this figure be a square.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B Q17
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 30

Question 18.
Write two conditions that will make the adjoining figure a square.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B Q18
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 27 Quadrilateral Ex 27B 31

Selina Concise Mathematics Class 6 ICSE Solutions