M l aggarwal understanding icse mathematics class 8 Solutions for Chapter 13 understanding quadrilaterals

Some figures are given below.

Classify each of them on the basis of the following:

(a) Simple curve

(b) Simple closed curve

(c) Polygon

(d) Convex polygon

(e) Concave polygon

How many diagonals does each of the following have?

(a) A convex quadrilateral

(b) A regular hexagon

Find the sum of measures of all interior angles of a polygon with the number of

sides:

(i) 8

(ii) 12

Find the number of sides of a regular polygon whose each exterior angles has a measure of

(i) 24^{\circ} (ii) 60^{\circ} (iii) 72 ^{\circ}

Find the number of sides of a regular polygon if each of its interior angles is

(i) 90^{\circ} (ii) 108^{\circ} (iii) 165^{\circ}

Find the number of sides in a polygon if the sum of its interior angles is:

(i) 1260^{\circ} (ii) 1980^{\circ} (iii) 3420^{\circ}

If the angles of a pentagon are in the ratio 7 : 8 : 11 : 13 : 15, find the angles.

The angles of a pentagon are x^{\circ},(x-10)^{\circ},(x+20)^{\circ},(2 x-44)^{\circ} \text { and }(2 x-70)^{\circ}

The exterior angles of a pentagon are in ratio 1 : 2 : 3 : 4 : 5. Find all the interior angles of the pentagon.

In a quadrilateral ABCD, AB || DC. If ∠A : ∠D = 2:3 and ∠B : ∠C = ∠7 : 8, find the measure of each angle.

From the adjoining figure, find

(i) x

(ii) ∠DAB

(iii) ∠ADB

Find the angle measure x in the following figures

(i) In the given figure, find x + y + z.

A heptagon has three equal angles each of 120 and four equal angles. Find the

size of equal angles.

The ratio between an exterior angle and the interior angle of a regular polygon is 1

: 5. Find

(i) the measure of each exterior angle

(ii) the measure of each interior angle

(iii) the number of sides in the polygon

Each interior angle of a regular polygon is double of its exterior angle. Find the

number of sides in the polygon

In the given figure, ABCD is a parallelogram. Complete each statement along with

the definition or property used.

(i) AD = ………..

(ii) DC = ………..

(iii) ∠DCB = ………..

(iv) ∠ADC = ………..

(v) ∠DAB = ………..

(vi) OC = ………..

(vii) OB = ………..

(viii) m∠DAB + m∠CDA = ………..

Consider the following parallelograms. Find the values of x, y, z in each.

(i)

Two adjacent sides of a parallelogram are in the ratio 5 : 7. If the perimeter of a

parallelogram is 72 cm, find the length of its sides.

The measure of two adjacent angles of a parallelogram is in the ratio 4: 5. Find the

measure of each angle of the parallelogram.

Can a quadrilateral ABCD be a parallelogram, give reasons in support of your

answer.

(i) ∠A + ∠C= 180o?

(ii) AD = BC = 6 cm, AB = 5 cm, DC = 4.5 cm?

(iii) ∠B = 80o, ∠D = 70o?

(iv) ∠B + ∠C= 180o?

In the following figures, HOPE and ROPE are parallelograms. Find the measures of

angles x, y and z. State the properties you use to find them.

,

In the given figure TURN and BURN are parallelograms. Find the measures of x and y

(lengths are in cm).

In the following figure, both ABCD and PQRS are parallelograms. Find the value of x.

In the given figure, ABCD, is a parallelogram and diagonals intersect at O. Find :

(i) ∠CAD

(ii) ∠ACD

(iii) ∠ADC

In the given figure, ABCD is a parallelogram. Perpendiculars DN and BP are drawn

on diagonal AC. Prove that:

(i) ΔDCN ≅ ΔBAP

(ii) AN = CP

In the given figure, ABC is a triangle. Through A, B, and C lines are drawn parallel to

BC, CA, and AB respectively, which form a ΔPQR.

Show that 2(AB + BC + CA) = PQ + QR + RP

Identify all the quadrilaterals that have

(i) four sides of equal length

(ii) four right angles.

Explain how a square is

(i) a quadrilateral

(ii) a parallelogram

(iii) a rhombus

(iv) a rectangle

Name the quadrilaterals whose diagonals

(i) bisect each other

(ii) are perpendicular bisectors of each other

(iii) are equal

In the given figure, ABCD is a rhombus, find the values of x, y and z

,

In the given figure, ABCD is a trapezium. If ∠A : ∠D = 5 : 7, ∠B = (3x + 11)o and ∠C =

(5x – 31)o, then find all the angles of the trapezium.

In the given figure, ABCD is a rectangle. If ∠CEB : ∠ECB = 3 : 2 find

(i) ∠CEB,

(ii) ∠DCF

In the given figure, ABCD is a rectangle and diagonals intersect at O. If ∠AOB = 118o,

find

(i) ∠ABO

(ii) ∠ADO

(iii) ∠OCB

In the given figure, ABCD is a rhombus and ∠ABD = 50. Find :

(i) ∠CAB

(ii) ∠BCD

(iii) ∠ADC

In the given isosceles trapezium ABCD, ∠C = 102. Find all the remaining angles of

the trapezium.

In the given figure, PQRS is a kite. Find the values of x and y.