# NCERT solutions for Mathematics Exemplar Class 8 chapter 5 - Understanding Quadrilaterals and Practical Geometry [Latest edition]

#### Chapters ## Chapter 5: Understanding Quadrilaterals and Practical Geometry

Exercise
Exercise [Pages 144 - 163]

### NCERT solutions for Mathematics Exemplar Class 8 Chapter 5 Understanding Quadrilaterals and Practical Geometry Exercise [Pages 144 - 163]

#### Choose the correct alternative:

Exercise | Q 1 | Page 144

If three angles of a quadrilateral are each equal to 75°, the fourth angle is ______.

• 150°

• 135°

• 45°

• 75°

Exercise | Q 2 | Page 144

For which of the following, diagonals bisect each other?

• Square

• Kite

• Trapezium

Exercise | Q 3 | Page 144

For which of the following figures, all angles are equal?

• Rectangle

• Kite

• Trapezium

• Rhombus

Exercise | Q 4 | Page 144

For which of the following figures, diagonals are perpendicular to each other?

• Parallelogram

• Kite

• Trapezium

• Rectangle

Exercise | Q 5 | Page 144

For which of the following figures, diagonals are equal?

• Trapezium

• Rhombus

• Parallelogram

• Rectangle

Exercise | Q 6 | Page 144

Which of the following figures satisfy the following properties?
- All sides are congruent.
- All angles are right angles.
- Opposite sides are parallel.

• • • • Exercise | Q 7 | Page 145

Which of the following figures satisfy the following property?
- Has two pairs of congruent adjacent sides.

• • • • Exercise | Q 8 | Page 145

Which of the following figures satisfy the following property?
- Only one pair of sides are parallel.

• • • • Exercise | Q 9 | Page 145

Which of the following figures do not satisfy any of the following properties?
- All sides are equal.
- All angles are right angles.
- Opposite sides are parallel.

• • • • Exercise | Q 10 | Page 145

Which of the following properties describe a trapezium?

• A pair of opposite sides is parallel

• The diagonals bisect each other

• The diagonals are perpendicular to each other

• The diagonals are equal

Exercise | Q 11 | Page 146

Which of the following is a property of a parallelogram?

• Opposite sides are parallel

• The diagonals bisect each other at right angles

• The diagonals are perpendicular to each other

• All angles are equal

Exercise | Q 12 | Page 146

What is the maximum number of obtuse angles that a quadrilateral can have?

• 1

• 2

• 3

• 4

Exercise | Q 13 | Page 146

How many non-overlapping triangles can we make in a n-gon (polygon having n sides), by joining the vertices?

• n – 1

• n – 2

• n – 3

• n – 4

Exercise | Q 14 | Page 146

What is the sum of all the angles of a pentagon?

• 180°

• 360°

• 540°

• 720°

Exercise | Q 15 | Page 146

What is the sum of all angles of a hexagon?

• 180°

• 360°

• 540°

• 720°

Exercise | Q 16 | Page 146

If two adjacent angles of a parallelogram are (5x – 5)° and (10x + 35)°, then the ratio of these angles is ______.

• 1 : 3

• 2 : 3

• 1 : 4

• 1 : 2

Exercise | Q 17 | Page 146

A quadrilateral whose all sides are equal, opposite angles are equal and the diagonals bisect each other at right angles is a ______.

• Rhombus

• Parallelogram

• Square

• Rectangle

Exercise | Q 18 | Page 146

A quadrilateral whose opposite sides and all the angles are equal is a ______.

• Rectangle

• Parallelogram

• Square

• Rhombus

Exercise | Q 19 | Page 146

A quadrilateral whose all sides, diagonals and angles are equal is a ______.

• Square

• Trapezium

• Rectangle

• Rhombus

Exercise | Q 20 | Page 147

How many diagonals does a hexagon have?

• 9

• 8

• 2

• 6

Exercise | Q 21 | Page 147

If the adjacent sides of a parallelogram are equal then parallelogram is a ______.

• Rectangle

• Trapezium

• Rhombus

• Square

Exercise | Q 22 | Page 147

If the diagonals of a quadrilateral are equal and bisect each other, then the quadrilateral is a ______.

• Rhombus

• Rectangle

• Square

• Parallelogram

Exercise | Q 23 | Page 147

The sum of all exterior angles of a triangle is ______.

• 180°

• 360°

• 540°

• 720°

Exercise | Q 24 | Page 147

Which of the following is an equiangular and equilateral polygon?

• Square

• Rectangle

• Rhombus

• Right triangle

Exercise | Q 25 | Page 147

Which one has all the properties of a kite and a parallelogram?

• Trapezium

• Rhombus

• Rectangle

• Parallelogram

Exercise | Q 26 | Page 147

The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. The smallest angle is ______.

• 72°

• 144°

• 36°

• 18°

Exercise | Q 27 | Page 147

In the trapezium ABCD, the measure of ∠D is ______. • 55°

• 115°

• 135°

• 125°

Exercise | Q 28 | Page 147

A quadrilateral has three acute angles. If each measures 80°, then the measure of the fourth angle is ______.

• 150°

• 120°

• 105°

• 140°

Exercise | Q 29 | Page 147

The number of sides of a regular polygon where each exterior angle has a measure of 45° is ______.

• 8

• 10

• 4

• 6

Exercise | Q 30 | Page 148

In a parallelogram PQRS, if ∠P = 60°, then other three angles are ______.

• 45°, 135°, 120°

• 60°, 120°, 120°

• 60°, 135°, 135°

• 45°, 135°, 135°

Exercise | Q 31 | Page 148

If two adjacent angles of a parallelogram are in the ratio 2 : 3, then the measure of angles are ______.

• 72°, 108°

• 36°, 54°

• 80°, 120°

• 96°, 144°

Exercise | Q 32 | Page 148

If PQRS is a parallelogram, then ∠P – ∠R is equal to ______.

• 60°

• 90°

• 80°

Exercise | Q 33 | Page 148

The sum of adjacent angles of a parallelogram is ______.

• 180°

• 120°

• 360°

• 90°

Exercise | Q 34 | Page 148

The angle between the two altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is 30°. The measure of the obtuse angle is ______.

• 100°

• 150°

• 105°

• 120°

Exercise | Q 35 | Page 148

In the given figure, ABCD and BDCE are parallelograms with common base DC. If BC ⊥ BD, then ∠BEC = ______. • 60°

• 30°

• 150°

• 120°

Exercise | Q 36 | Page 148

Length of one of the diagonals of a rectangle whose sides are 10 cm and 24 cm is ______.

• 25 cm

• 20 cm

• 26 cm

• 3.5 cm

Exercise | Q 37 | Page 148

If the adjacent angles of a parallelogram are equal, then the parallelogram is a ______.

• Rectangle

• Trapezium

• Rhombus

• Any of the three

Exercise | Q 38 | Page 148

Which of the following can be four interior angles of a quadrilateral?

• 140°, 40°, 20°, 160°

• 270°, 150°, 30°, 20°

• 40°, 70°, 90°, 60°

• 110°, 40°, 30°, 180°

Exercise | Q 39 | Page 149

The sum of angles of a concave quadrilateral is ______.

• More than 360°

• Less than 360°

• Equal to 360°

• Twice of 360°

Exercise | Q 40 | Page 149

Which of the following can never be the measure of exterior angle of a regular polygon?

• 22°

• 36°

• 45°

• 30°

Exercise | Q 41 | Page 149

In the figure, BEST is a rhombus, Then the value of y – x is ______. • 40°

• 50°

• 20°

• 10°

Exercise | Q 42 | Page 149

The closed curve which is also a polygon is ______.

• • • • Exercise | Q 43 | Page 149

Which of the following is not true for an exterior angle of a regular polygon with n sides?

• Each exterior angle = 360^circ/n

• Exterior angle = 180° – interior angle

• n = 360^circ/"exterior angle"

• Each exterior angle = ((n - 2) xx 180^circ)/n

Exercise | Q 44 | Page 149

PQRS is a square. PR and SQ intersect at O. Then ∠POQ is a ______.

• Right angle

• Straight angle

• Reflex angle

• Complete angle

Exercise | Q 45 | Page 150

Two adjacent angles of a parallelogram are in the ratio 1:5. Then all the angles of the parallelogram are ______.

• 30°, 150°, 30°, 150°

• 85°, 95°, 85°, 95°

• 45°, 135°, 45°, 135°

• 30°, 180°, 30°, 180°

Exercise | Q 46 | Page 150

A parallelogram PQRS is constructed with sides QR = 6 cm, PQ = 4 cm and ∠PQR = 90°. Then PQRS is a ______.

• Square

• Rectangle

• Rhombus

• Trapezium

Exercise | Q 47 | Page 150

The angles P, Q, R and S of a quadrilateral are in the ratio 1:3:7:9. Then PQRS is a ______.

• Parallelogram

• Trapezium with PQ || RS

• Trapezium with QR || PS

• kite

Exercise | Q 48 | Page 150

PQRS is a trapezium in which PQ || SR and ∠P = 130°, ∠Q = 110°. Then ∠R is equal to ______.

• 70°

• 50°

• 65°

• 55°

Exercise | Q 49 | Page 150

The number of sides of a regular polygon whose each interior angle is of 135° is ______.

• 6

• 7

• 8

• 9

Exercise | Q 50 | Page 150

If a diagonal of a quadrilateral bisects both the angles, then it is a ______.

• Kite

• Parallelogram

• Rhombus

• Rectangle

Exercise | Q 51 | Page 150

To construct a unique parallelogram, the minimum number of measurements required is ______.

• 2

• 3

• 4

• 5

Exercise | Q 52 | Page 150

To construct a unique rectangle, the minimum number of measurements required is ______.

• 4

• 3

• 2

• 1

#### Fill in the blanks:

Exercise | Q 53 | Page 150

In quadrilateral HOPE, the pairs of opposite sides are ______.

Exercise | Q 54 | Page 150

Exercise | Q 55 | Page 150

In quadrilateral WXYZ, the pairs of opposite angles are ______.

Exercise | Q 56 | Page 151

The diagonals of the quadrilateral DEFG are ______ and ______.

Exercise | Q 57 | Page 151

The sum of all ______ of a quadrilateral is 360°.

Exercise | Q 58 | Page 151

The measure of each exterior angle of a regular pentagon is ______.

Exercise | Q 59 | Page 151

Sum of the angles of a hexagon is ______.

Exercise | Q 60 | Page 151

The measure of each exterior angle of a regular polygon of 18 sides is ______.

Exercise | Q 61 | Page 151

The number of sides of a regular polygon, where each exterior angle has a measure of 36°, is ______.

Exercise | Q 62 | Page 151 is a closed curve entirely made up of line segments. The another name for this shape is ______.

Exercise | Q 63 | Page 151

A quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure is ______.

Exercise | Q 64 | Page 151

The measure of each angle of a regular pentagon is ______.

Exercise | Q 65 | Page 151

The name of three-sided regular polygon is ______.

Exercise | Q 66 | Page 151

The number of diagonals in a hexagon is ______.

Exercise | Q 67 | Page 151

A polygon is a simple closed curve made up of only ______.

Exercise | Q 68 | Page 151

A regular polygon is a polygon whose all sides are equal and all ______ are equal.

Exercise | Q 69 | Page 151

The sum of interior angles of a polygon of n sides is ______ right angles.

Exercise | Q 70 | Page 151

The sum of all exterior angles of a polygon is ______.

Exercise | Q 71 | Page 151

Exercise | Q 72 | Page 151

A quadrilateral in which a pair of opposite sides is parallel is ______.

Exercise | Q 73 | Page 151

If all sides of a quadrilateral are equal, it is a ______.

Exercise | Q 74 | Page 151

In a rhombus diagonals intersect at ______ angles.

Exercise | Q 75 | Page 151

______ measurements can determine a quadrilateral uniquely.

Exercise | Q 76 | Page 152

A quadrilateral can be constructed uniquely if its three sides and ______ angles are given.

Exercise | Q 77 | Page 152

A rhombus is a parallelogram in which ______ sides are equal.

Exercise | Q 78 | Page 152

The measure of ______ angle of concave quadrilateral is more than 180°.

Exercise | Q 79 | Page 152

A diagonal of a quadrilateral is a line segment that joins two ______ vertices of the quadrilateral.

Exercise | Q 80 | Page 152

The number of sides in a regular polygon having measure of an exterior angle as 72° is ______.

Exercise | Q 81 | Page 152

If the diagonals of a quadrilateral bisect each other, it is a ______.

Exercise | Q 82 | Page 152

The adjacent sides of a parallelogram are 5 cm and 9 cm. Its perimeter is ______.

Exercise | Q 83 | Page 152

A nonagon has ______ sides.

Exercise | Q 84 | Page 152

Diagonals of a rectangle are ______.

Exercise | Q 85 | Page 152

A polygon having 10 sides is known as ______.

Exercise | Q 86 | Page 152

A rectangle whose adjacent sides are equal becomes a ______.

Exercise | Q 87 | Page 152

If one diagonal of a rectangle is 6 cm long, length of the other diagonal is ______.

Exercise | Q 88 | Page 152

Adjacent angles of a parallelogram are ______.

Exercise | Q 89 | Page 152

If only one diagonal of a quadrilateral bisects the other, then the quadrilateral is known as ______.

Exercise | Q 90 | Page 152

In trapezium ABCD with AB || CD, if ∠A = 100°, then ∠D = ______.

Exercise | Q 91 | Page 152

The polygon in which sum of all exterior angles is equal to the sum of interior angles is called ______.

#### State whether the following statement is True or False:

Exercise | Q 92 | Page 152

All angles of a trapezium are equal.

• True

• False

Exercise | Q 93 | Page 152

All squares are rectangles.

• True

• False

Exercise | Q 94 | Page 152

All kites are squares.

• True

• False

Exercise | Q 95 | Page 152

All rectangles are parallelograms.

• True

• False

Exercise | Q 96 | Page 153

All rhombuses are squares.

• True

• False

Exercise | Q 97 | Page 153

Sum of all the angles of a quadrilateral is 180°.

• True

• False

Exercise | Q 98 | Page 153

• True

• False

Exercise | Q 99 | Page 153

Triangle is a polygon whose sum of exterior angles is double the sum of interior angles.

• True

• False

Exercise | Q 100 | Page 153 is a polygon.

• True

• False

Exercise | Q 101 | Page 153

A kite is not a convex quadrilateral.

• True

• False

Exercise | Q 102 | Page 153

The sum of interior angles and the sum of exterior angles taken in an order are equal in case of quadrilaterals only.

• True

• False

Exercise | Q 103 | Page 153

If the sum of interior angles is double the sum of exterior angles taken in an order of a polygon, then it is a hexagon.

• True

• False

Exercise | Q 104 | Page 153

A polygon is regular if all of its sides are equal.

• True

• False

Exercise | Q 105 | Page 153

• True

• False

Exercise | Q 106 | Page 153

If diagonals of a quadrilateral are equal, it must be a rectangle.

• True

• False

Exercise | Q 107 | Page 153

If opposite angles of a quadrilateral are equal, it must be a parallelogram.

• True

• False

Exercise | Q 108 | Page 153

The interior angles of a triangle are in the ratio 1:2:3, then the ratio of its exterior angles is 3:2:1.

• True

• False

Exercise | Q 109 | Page 153 is a concave pentagon

• True

• False

Exercise | Q 110 | Page 153

Diagonals of a rhombus are equal and perpendicular to each other.

• True

• False

Exercise | Q 111 | Page 153

Diagonals of a rectangle are equal.

• True

• False

Exercise | Q 112 | Page 153

Diagonals of rectangle bisect each other at right angles.

• True

• False

Exercise | Q 113 | Page 153

Every kite is a parallelogram.

• True

• False

Exercise | Q 114 | Page 154

Every trapezium is a parallelogram.

• True

• False

Exercise | Q 115 | Page 154

Every parallelogram is a rectangle.

• True

• False

Exercise | Q 116 | Page 154

Every trapezium is a rectangle.

• True

• False

Exercise | Q 117 | Page 154

Every rectangle is a trapezium.

• True

• False

Exercise | Q 118 | Page 154

Every square is a rhombus.

• True

• False

Exercise | Q 119 | Page 154

Every square is a parallelogram.

• True

• False

Exercise | Q 120 | Page 154

Every square is a trapezium.

• True

• False

Exercise | Q 121 | Page 154

Every rhombus is a trapezium

• True

• False

Exercise | Q 122 | Page 154

A quadrilateral can be drawn if only measures of four sides are given.

• True

• False

Exercise | Q 123 | Page 154

A quadrilateral can have all four angles as obtuse.

• True

• False

Exercise | Q 124 | Page 154

A quadrilateral can be drawn if all four sides and one diagonal is known.

• True

• False

Exercise | Q 125 | Page 154

A quadrilateral can be drawn when all the four angles and one side is given.

• True

• False

Exercise | Q 126 | Page 154

A quadrilateral can be drawn if all four sides and one angle is known.

• True

• False

Exercise | Q 127 | Page 154

A quadrilateral can be drawn if three sides and two diagonals are given.

• True

• False

Exercise | Q 128 | Page 154

If diagonals of a quadrilateral bisect each other, it must be a parallelogram.

• True

• False

Exercise | Q 129 | Page 154

A quadrilateral can be constructed uniquely if three angles and any two sides are given.

• True

• False

Exercise | Q 130 | Page 154

A parallelogram can be constructed uniquely if both diagonals and the angle between them is given.

• True

• False

Exercise | Q 131 | Page 154

A rhombus can be constructed uniquely if both diagonals are given.

• True

• False

#### Solve the following:

Exercise | Q 132 | Page 154

The diagonals of a rhombus are 8 cm and 15 cm. Find its side.

Exercise | Q 133 | Page 154

Two adjacent angles of a parallelogram are in the ratio 1:3. Find its angles.

Exercise | Q 134 | Page 154

Of the four quadrilaterals-square, rectangle, rhombus and trapezium-one is somewhat different from the others because of its design. Find it and give justification.

Exercise | Q 135 | Page 155

In a rectangle ABCD, AB = 25 cm and BC = 15. In what ratio does the bisector of ∠C divide AB?

Exercise | Q 136 | Page 155

PQRS is a rectangle. The perpendicular ST from S on PR divides ∠S in the ratio 2:3. Find ∠TPQ.

Exercise | Q 137 | Page 155

A photo frame is in the shape of a quadrilateral. With one diagonal longer than the other. Is it a rectangle? Why or why not?

Exercise | Q 138 | Page 155

The adjacent angles of a parallelogram are (2x – 4)° and (3x – 1)°. Find the measures of all angles of the parallelogram.

Exercise | Q 139 | Page 155

The point of intersection of diagonals of a quadrilateral divides one diagonal in the ratio 1:2. Can it be a parallelogram? Why or why not?

Exercise | Q 140 | Page 155

The ratio between exterior angle and interior angle of a regular polygon is 1:5. Find the number of sides of the polygon.

Exercise | Q 141 | Page 155

Two sticks each of length 5 cm are crossing each other such that they bisect each other. What shape is formed by joining their endpoints? Give reason.

Exercise | Q 142 | Page 155

Two sticks each of length 7 cm are crossing each other such that they bisect each other at right angles. What shape is formed by joining their end points? Give reason.

Exercise | Q 143 | Page 155

A playground in the town is in the form of a kite. The perimeter is 106 metres. If one of its sides is 23 metres, what are the lengths of other three sides?

Exercise | Q 144 | Page 155 Exercise | Q 145 | Page 156

In rectangle PAIR, find ∠ARI, ∠RMI and ∠PMA. Exercise | Q 146 | Page 156

In parallelogram ABCD, find ∠B, ∠C and ∠D. Exercise | Q 147 | Page 156

In parallelogram PQRS, O is the mid point of SQ. Find ∠S, ∠R, PQ, QR and diagonal PR. Exercise | Q 148 | Page 156

In rhombus BEAM, find ∠AME and ∠AEM. Exercise | Q 149 | Page 156

In parallelogram FIST, find ∠SFT, ∠OST and ∠STO. Exercise | Q 150 | Page 157

In the given parallelogram YOUR, ∠RUO = 120° and OY is extended to point S such that ∠SRY = 50°. Find ∠YSR. Exercise | Q 151 | Page 157

In kite WEAR, ∠WEA = 70° and ∠ARW = 80°. Find the remaining two angles. Exercise | Q 152.(i) | Page 157

A rectangular MORE is shown below: Answer the following questions by giving appropriate reason.
Is RE = OM?

Exercise | Q 152.(ii) | Page 157

A rectangular MORE is shown below: Answer the following questions by giving appropriate reason.
Is ∠MYO = ∠RXE?

Exercise | Q 152.(iii) | Page 157

A rectangular MORE is shown below: Answer the following questions by giving appropriate reason.
Is ∠MOY = ∠REX?

Exercise | Q 152.(iv) | Page 157

A rectangular MORE is shown below: Answer the following questions by giving appropriate reason.
Is ∆MYO ≅ ∆RXE?

Exercise | Q 152.(v) | Page 157

A rectangular MORE is shown below: Answer the following questions by giving appropriate reason.
Is MY = RX?

Exercise | Q 153 | Page 158

In parallelogram LOST, SN⊥OL and SM⊥LT. Find ∠STM, ∠SON and ∠NSM. Exercise | Q 154 | Page 158

In trapezium HARE, EP and RP are bisectors of ∠E and ∠R respectively. Find ∠HAR and ∠EHA. Exercise | Q 155 | Page 158

In parallelogram MODE, the bisector of ∠M and ∠O meet at Q, find the measure of ∠MQO.

Exercise | Q 156 | Page 158

A playground is in the form of a rectangle ATEF. Two players are standing at the points F and B where EF = EB. Find the values of x and y. Exercise | Q 157 | Page 158

In the following figure of a ship, ABDH and CEFG are two parallelograms. Find the value of x. Exercise | Q 158 | Page 159

A Rangoli has been drawn on a flor of a house. ABCD and PQRS both are in the shape of a rhombus. Find the radius of semicircle drawn on each side of rhombus ABCD. Exercise | Q 159 | Page 159

ABCDE is a regular pentagon. The bisector of angle A meets the side CD at M. Find ∠AMC. Exercise | Q 160 | Page 159

Quadrilateral EFGH is a rectangle in which J is the point of intersection of the diagonals. Find the value of x if JF = 8x + 4 and EG = 24x – 8.

Exercise | Q 161 | Page 159

Find the values of x and y in the following parallelogram. Exercise | Q 162 | Page 160

Find the values of x and y in the following kite. Exercise | Q 163 | Page 160

Find the value of x in the trapezium ABCD given below. Exercise | Q 164 | Page 160

Two angles of a quadrilateral are each of measure 75° and the other two angles are equal. What is the measure of these two angles? Name the possible figures so formed.

Exercise | Q 165 | Page 160

In a quadrilateral PQRS, ∠P = 50°, ∠Q = 50°, ∠R = 60°. Find ∠S. Is this quadrilateral convex or concave?

Exercise | Q 166 | Page 160

Both the pairs of opposite angles of a quadrilateral are equal and supplementary. Find the measure of each angle.

Exercise | Q 167 | Page 160

Find the measure of each angle of a regular octagon.

Exercise | Q 168 | Page 160

Find the measure of an are exterior angle of a regular pentagon and an exterior angle of a regular decagon. What is the ratio between these two angles?

Exercise | Q 169 | Page 160

In the figure, find the value of x. Exercise | Q 170 | Page 161

Three angles of a quadrilateral are equal. Fourth angle is of measure 120°. What is the measure of equal angles?

Exercise | Q 171 | Page 161

In a quadrilateral HOPE, PS and ES are bisectors of ∠P and ∠E respectively. Give reason

Exercise | Q 172 | Page 161

ABCD is a parallelogram. Find the value of x, y and z. Exercise | Q 173 | Page 161

Diagonals of a quadrilateral are perpendicular to each other. Is such a quadrilateral always a rhombus? Give a figure to justify your answer.

Exercise | Q 174 | Page 161

ABCD is a trapezium such that AB||CD, ∠A:∠D = 2 :1, ∠B:∠C = 7:5. Find the angles of the trapezium.

Exercise | Q 175 | Page 161

A line l is parallel to line m and a transversal p intersects them at X, Y respectively. Bisectors of interior angles at X and Y interesct at P and Q. Is PXQY a rectangle? Given reason.

Exercise | Q 176 | Page 161

ABCD is a parallelogram. The bisector of angle A intersects CD at X and bisector of angle C intersects AB at Y. Is AXCY a parallelogram? Give reason.

Exercise | Q 177 | Page 161

A diagonal of a parallelogram bisects an angle. Will it also bisect the other angle? Give reason.

Exercise | Q 178 | Page 161

The angle between the two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 45°. Find the angles of the parallelogram.

Exercise | Q 179 | Page 161

ABCD is a rhombus such that the perpendicular bisector of AB passes through D. Find the angles of the rhombus.

Exercise | Q 180 | Page 161

ABCD is a parallelogram. Points P and Q are taken on the sides AB and AD respectively and the parallelogram PRQA is formed. If ∠C = 45°, find ∠R.

Exercise | Q 181 | Page 162

In parallelogram ABCD, the angle bisector of ∠A bisects BC. Will angle bisector of B also bisect AD? Give reason.

Exercise | Q 182 | Page 162

A regular pentagon ABCDE and a square ABFG are formed on opposite sides of AB. Find ∠BCF.

Exercise | Q 183 | Page 162

Find maximum number of acute angles which a convex, a quadrilateral, a pentagon and a hexagon can have. Observe the pattern and generalise the result for any polygon.

Exercise | Q 184 | Page 162

In the following figure, FD || BC || AE and AC || ED. Find the value of x. Exercise | Q 185 | Page 162

In the following figure, AB || DC and AD = BC. Find the value of x. Exercise | Q 186 | Page 162

Construct a trapezium ABCD in which AB||DC, ∠A = 105°, AD = 3 cm, AB = 4 cm and CD = 8 cm.

Exercise | Q 187 | Page 162

Construct a parallelogram ABCD in which AB = 4 cm, BC = 5 cm and ∠B = 60°.

Exercise | Q 188 | Page 162

Construct a rhombus whose side is 5 cm and one angle is of 60°.

Exercise | Q 189 | Page 162

Construct a rectangle whose one side is 3 cm and a diagonal equal to 5 cm

Exercise | Q 190 | Page 162

Construct a square of side 4 cm.

Exercise | Q 191 | Page 162

Construct a rhombus CLUE in which CL = 7.5 cm and LE = 6 cm.

Exercise | Q 192 | Page 162

Construct a quadrilateral BEAR in which BE = 6 cm, EA = 7 cm, RB = RE = 5 cm and BA = 9 cm. Measure its fourth side.

Exercise | Q 193 | Page 163

Construct a parallelogram POUR in which, PO = 5.5 cm, OU = 7.2 cm and ∠O = 70°.

Exercise | Q 194 | Page 163

Draw a circle of radius 3 cm and draw its diameter and label it as AC. Construct its perpendicular bisector and let it intersect the circle at B and D. What type of quadrilateral is ABCD? Justify your answer.

Exercise | Q 195 | Page 163

Construct a parallelogram HOME with HO = 6 cm, HE = 4 cm and OE = 3 cm.

Exercise | Q 196 | Page 163

Is it possible to construct a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 5.4 cm, DA = 5.9 cm and diagonal AC = 8 cm? If not, why?

Exercise | Q 197 | Page 163

Is it possible to construct a quadrilateral ROAM in which RO = 4 cm, OA = 5 cm, ∠O = 120°, ∠R = 105° and ∠A = 135°? If not, why?

Exercise | Q 198 | Page 163

Construct a square in which each diagonal is 5cm long.

Exercise | Q 199 | Page 163

Construct a quadrilateral NEWS in which NE = 7 cm, EW = 6 cm, ∠N = 60°, ∠E = 110° and ∠S = 85°.

Exercise | Q 200 | Page 163

Construct a parallelogram when one of its side is 4 cm and its two diagonals are 5.6 cm and 7 cm. Measure the other side.

Exercise | Q 201 | Page 163

Find the measure of each angle of a regular polygon of 20 sides?

Exercise | Q 202 | Page 163

Construct a trapezium RISK in which RI || KS, RI = 7 cm, IS = 5 cm, RK = 6.5 cm and ∠I = 60°.

Exercise | Q 203 | Page 163

Construct a trapezium ABCD where AB || CD, AD = BC = 3.2 cm, AB = 6.4 cm and CD = 9.6 cm. Measure ∠B and ∠A. ## Chapter 5: Understanding Quadrilaterals and Practical Geometry

Exercise ## NCERT solutions for Mathematics Exemplar Class 8 chapter 5 - Understanding Quadrilaterals and Practical Geometry

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