## 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:

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:

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:

Question 4.

Use the information given in the following figure to find :

(i) x

(ii) ∠B and ∠C

Solution:

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:

Question 6.

From the following figure find ;

(i) x,

(ii) ∠ABC,

(iii) ∠ACD.

Solution:

Question 7.

Given : In quadrilateral ABCD ; ∠C = 64°, ∠D = ∠C – 8° ;

∠A = 5(a+2)° and ∠B = 2(2a+7)°.

Calculate ∠A.

Solution:

Question 8.

In the given figure :

∠b = 2a + 15

and ∠c = 3a+5; find the values of b and c.

Solution:

Question 9.

Three angles of a quadrilateral are equal. If the fourth angle is 69°; find the measure of equal angles.

Solution:

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:

Question 11.

Use the information given in the following figure to find the value of x.

Solution:

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.

Solution:

### 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:

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:

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:

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:

Question 5.

Two diagonals of an isosceles trapezium are x cm and (3x – 8) cm. Find the value of x.

Solution:

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Question 6.

Angle A of an isosceles trapezium is 115° ; find the angles B, C and D.

Solution:

Question 7.

Two opposite angles of a parallelogram are 100° each. Find each of the other two opposite angles.

Solution:

Question 8.

Two adjacent angles of a parallelogram are 70° and 110° respectively. Find the other two angles of it.

Solution:

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:

Question 10.

In a parallelogram ABCD, its diagonals AC and BD intersect each other at point O.

If AC = 12 cm and BD = 9 cm ; find; lengths of OA and OD.

Solution:

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.

Solution:

Question 12.

In parallelogram ABCD, ∠A = 90°

(i) What is the measure of angle B.

(ii) Write the special name of the paralleogram.

Solution:

Question 13.

One diagnol of a rectangle is 18 cm. What is the length of its other diagnol?

Solution:

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.

Solution:

Question 15.

If three angles of a quadrilateral are 90° each, show that the given quadrilateral is a rectangle.

Solution:

Question 16.

The diagnols of a rhombus are 6 .cm and 8 cm. State the angle at which these diagnols intersect.

Solution:

Question 17.

Write, giving reason, the name of the figure drawn alongside. Under what condition will this figure be a square.

Solution:

Question 18.

Write two conditions that will make the adjoining figure a square.

Solution: