Selina solutions concise mathematics class 6 icse Solutions for Chapter 27 quadrilateral

Exercises in Chapter 27 quadrilateral Grade 6

Exercise 27(A)

Exercise 27(B)

Questions in Exercise 27(A)

Q1) Two angles of a quadrilateral are 89° and 113°. If the other two angles are equal; find the equal angles.

Q2) 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.

Q3) 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.

Q4) Use the information given in the following figure to find :

(i) x

(ii) ∠B and ∠C

Q5) 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.

Q6) From the following figure find ;

(i) x,

(ii) ∠ABC,

(iii) ∠ACD.

Q7) Given : In quadrilateral ABCD ; ∠C = 64°, ∠D = ∠C – 8° ; ∠A = 5(a+2)° and ∠B = 2(2a+7)°. Calculate ∠A.

Q8) In the given figure :

∠b = 2a + 15

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

Q9) Three angles of a quadrilateral are equal. If the fourth angle is 69°; find the measure of equal angles.

Q10) 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 ?

Q11) Use the information given in the following figure to find the value of x.

Q12) 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.

Questions in Exercise 27(B)

Q1) In a trapezium ABCD, side AB is parallel to side DC. If ∠A = 78° and ∠C = 120°, find angles B and D.

Q2) In a trapezium ABCD, side AB is parallel to side DC. If ∠A = x° and ∠D = (3x – 20)°; find the value of x.

Q3) 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

Q4) In an isosceles trapezium one pair of opposite sides are ….. to each Other and the other pair of opposite sides are ….. to each other.

Q5) Two diagonals of an isosceles trapezium are x cm and (3x – 8) cm. Find the value of x.

Q6) Angle A of an isosceles trapezium is 115° ; find the angles B, C and D.

Q7) Two opposite angles of a parallelogram are 100° each. Find each of the other two opposite angles.

Q8) Two adjacent angles of a parallelogram are 70° and 110° respectively. Find the other two angles of it.

Q9) The angles A, B, C and D of a quadrilateral are in the ratio 2:3:2:3. Show this quadrilateral is a parallelorgram.

Q10) 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.

Q11) 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.

Q12) In parallelogram ABCD, ∠A = 90° (i) What is the measure of angle B. (ii) Write the special name of the paralleogram.

Q13) One diagonal of a rectangle is 18 cm. What is the length of its other diagonal?

Q14) 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.

Q15) If three angles of a quadrilateral are 90° each, show that the given quadrilateral is a rectangle.

Q16) The diagnols of a rhombus are 6 .cm and 8 cm. State the angle at which these diagnols intersect.

Q17) Write, giving reason, the name of the figure drawn alongside. Under what condition will this figure be a

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Chapters in this book

Number System (Consolidating the Sense of Numberness)

Estimation

Numbers in India and International System (With Comparison)

Place Value

Natural Numbers and Whole Numbers (Including Patterns)

Negative Numbers and Integers

Number Line

HCF and LCM

Playing with Numbers

Sets

Ratio

Proportion (Including Word Problems)

Unitary Method

Fractions

Decimal Fractions

Percent (Percentage)

Idea of Speed, Distance and Time

Fundamental Concepts (Algebra)

Fundamental Operations (Related to Algebraic Expressions)

Substitution (Including Use of Brackets as Grouping Symbols)

Framing Algebraic Expressions (Including Evaluation)

Simple (Linear) Equations (Including Word Problems)

Fundamental Concepts (Geometry)

Angles (With their Types)

Properties of Angles and Lines (Including Parallel Lines)

Triangles (Including Types, Properties and Construction)

Quadrilateral

Polygons

The Circle

Revision Exercise on Symmetry (Including Constructions on Symmetry)

Recognition of Solids

Perimeter and Area of Plane Figures

Data Handling (Including Pictograph and Bar Graph)

Mean and Median