Selina solutions for Mathematics [English] Class 6 chapter 27 - Quadrilateral [Latest edition]

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

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.

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.

Use the information given in the following figure to find :

(i) x
(ii) ∠B and ∠C

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

From the following figure find;

1. x
2. ∠ABC
3. ∠ACD

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

In the given figure : ∠b = 2a + 15 and ∠c = 3a + 5; find the values of b and c.

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

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
(i) Is PS also parallel to QR?
(ii) Assign a special name to quadrilateral PQRS.

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

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.

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

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

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.

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

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

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

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

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

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

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.

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.

In parallelogram ABCD, ∠A = 90°

(i) What is the measure of angle B.

(ii) Write the special name of the parallelogram.

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

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.

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

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

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

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