But, two angles need not be adjacent to be supplementary. In the next figure, ∠3 and ∠4 are supplementary, because their measures add to 180° . Show
Example 1: Two angles are supplementary. If the measure of the angle is twice the measure of the other, find the measure of each angle. If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. NCERT Exemplar Class 8 Maths Chapter 5 Understanding Quadrilaterals and Practical Geometry are part of NCERT Exemplar Class 8 Maths. Here we have given NCERT Exemplar Class 8 Maths Chapter 5 Understanding Quadrilaterals and Practical Geometry. NCERT Exemplar Class 8 Maths Chapter 5 Understanding Quadrilaterals and Practical GeometryMultiple Choice Questions Question. 2 For which of the following, diagonals bisect each other? Question. 3 In which of the following figures, all angles are equal? Question. 4 For which of the following figures, diagonals are perpendicular to each other? Question. 5 For which of the following figures, diagonals are equal? Question. 6 Which of the following figures satisfy the following properties? Solution. (c) We know that all the properties mentioned above are related to square and we can observe that figure R resembles a square. Question. 7 Which of the following figures satisfy the following property?Has two pairs of congruent adjacent sides. Solution. (c) We know that, a kite has two pairs of congruent adjacent sides and we can observe that figure R resembles a kite. Question. 8 Which of the following figures satisfy the following property? Solution. (a) We know that, in a trapezium, only one pair of sides are parallel and we can observe that figure P resembles a trapezium. Question. 9 Which of the following figures do not satisfy any of the following properties? Solution. (a) On observing the above figures, we conclude that the figure P does not satisfy any of the given properties. Question. 10 Which of the following properties describe a trapezium? Question. 11 Which of the following is a propefay of a parallelogram? Question. 12 What is the maximum number of obtuse angles that a quadrilateral can have? Question. 13 How many non-overlapping triangles can we make in a-n-gon (polygon having n sides), by joining the vertices? Question. 14 What is the sum of all the angles of a pentagon? Question. 15 What is the sum of all angles of a hexagon? Question. 16 If two adjacent angles of a parallelogram are (5x – 5) and (10x + 35), then the ratio of these angles is Question. 17 A quadrilateral whose all sides are equal, opposite angles are equal and Question. 18 A quadrilateral whose opposite sides and all the angles are equal is a Question. 19 A quadrilateral whose all sides, diagonals and angles are equal is a Question. 20 How many diagonals does a hexagon have? Question. 21 If the adjacent sides of a parallelogram are equal, then parallelogram is a Question. 22 If the diagonals of a quadrilateral are equal and bisect each other, then the quadrilateral is a Question. 23 The sum of all exterior angles of a triangle is Question. 24 Which of the following is an equiangular and equilateral polygon? Question. 25 Which one has all the properties of a kite and a parallelogram? Question. 26 The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. The smallest angle is Question. 27 In the trapezium ABCD, the measure of \(\angle D\) is Solution. Question. 28 A quadrilateral has three acute angles. If each measures 80°, then the measure of the fourth angle is Question. 29 The number of sides of a regular polygon where each exterior angle has a measure of 45° is Question. 30 In a parallelogram PQRS, if \(\angle P\) = 60°, then other three angles are Question. 31 If two adjacent angles of a parallelogram are in the ratio 2 : 3, then the measure of angles are Question. 32 IfPQRS is a parallelogram then \(\angle P\) – \(\angle R\) is equal to Question. 33 The sum of adjacent angles of a parallelogram is Question. 34 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 Question. 35 In the given figure, ABCD and BDCE are parallelograms with common base DC. If \(BC\bot BD\), then \(\angle BEC\) is equal to Solution. Question. 36 Length of one of the diagonals of a rectangle whose sides are 10 cm and 24 cm is Question. 37 If the adjacent angles of a parallelogram are equal, then the parallelogram is a (a) rectangle (b) trapezium (c) rhombus (d) None of these Question. 38 Which of the following can be four interior angles of a quadrilateral? Question. 39 The sum of angles of a concave quadrilateral is Question. 40 Which of the following can never be the measure of exterior angle of a regular polygon? (a) 22° (b) 36° (c)45° (d) 30° Question. 41 In the figure, BEST is a rhombus, then the value of y – x is Solution. Question. 42 The closed curve which is also a polygon, is Solution. (a) Figure (a) is polygon as no two line segments intersect each other. Question. 43 Which of the following is not true for an exterior angle of a regular polygon with n sides? Solution. (d) We know that, (a) and (b) are the formulae to find the measure of each exterior angle, when number of sides and measure of an interior angle respectively are given and (c) is the formula to find number of sides of polygon when exterior angle is given. Hence, the formula given in option (d) is not true for an exterior angle of a regular polygon with n sides. Question. 44 PQRS is a square. PR and SQ intersect at 0. Then, \(\angle POQ\) is a (a) right angle (b) straight angle (c) reflex angle (d) complete angle Question. 45 Two adjacent angles of a parallelogram are in the ratio 1 : 5. Then, all the angles of the parallelogram are Question. 46 A parallelogram PQRS is constructed with sides QR = 6 cm, PQ = 4 cm and \(\angle PQR\) = 90°. Then, PQRS is a Question. 47 The angles P, Q, R and 5 of a quadrilateral are in the ratio 1:3 :7:9. Then, PQRS is a Question. 48 PQRS is a trapezium in which PQ || SR and ZP = 130°, \(\angle Q\) = 110°. Then, \(\angle R\) is equal to. Question. 49 The number of sides of a regular polygon whose each interior angle is of 135° is (a) 6 (b) 7 (c) 8 (d) 9 Question. 50 If a diagonal of a quadrilateral bisects both the angles, then it is a Question. 51 To construct a unique parallelogram, the minimum number of measurements required is (a) 2 (b) 3 (c) 4 (d) 5 Question. 52 To construct a unique rectangle, the minimum number of measurements required is (a) 4 (b) 3 (0 2 (d) 1 Fill in the Blanks Question. 54 In quadrilateral ROPE, the pairs of adjacent angles are—————-. Question. 55 In quadrilateral WXYZ, the pairs of opposite angles are————–. Question . 56 The diagonals of the quadrilateral DEFG are———–and————–. Question. 57 The sum of all———— of a quadrilateral is 360°. Question. 58 The measure of each exterior angle of a regular pentagon is————— . Question. 59 Sum of the angles of a hexagon is———————-. Question. 60 The measure of each exterior angle of a regular polygon of 18 sides is———. Question. 61 The number of sides of a regular polygon, where each exterior angle has a measure of 36°, is—————-. Question. 62 Solution. concave polygon As one interior angle is of greater than 180°. Question. 63 A quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure is—————–. Question. 64 The measure of each angle of a regular pentagon is————–. Question. 65 The name of three-sided regular polygon is—————-. Question. 66 The number of diagonals in a hexagon is—————-. Question. 67 A polygon is a simple closed curve made up of only————. Question. 68 A regular polygon is a polygon whose all sides are equal and all———are equal. Question. 69 The sum of interior angles of a polygon of n sides is———- right angles. Question. 70 The sum of all exterior angles of a polygon is————. Question. 71 ————-is a regular quadrilateral. Question. 72 A quadrilateral in which a pair of opposite sides is parallel is————-. Question. 73 If all sides of a quadrilateral are equal, it is a————–. Question. 74 In a rhombus, diagonals intersect at———– angles. Question. 75 ———measurements can determine a quadrilateral uniquely. Question. 76 A quadrilateral can be constructed uniquely, if its three sides and———–angles are given. Question. 77 A rhombus is a parallelogram in which————sides are equal. Question. 78 The measure of——– angle of concave quadrilateral is more than 180°. Question. 79 A diagonal of a quadrilateral is a line segment that joins two——– vertices of the quadrilateral. Question. 80 The number of sides in a regular polygon having measure of an exterior angle as 72° is————— . Question. 81 If the diagonals of a quadrilateral bisect each other, it is a————. Question. 82 The adjacent sides of a parallelogram are 5 cm and 9 cm. Its perimeter is—–. Question. 83 A nonagon has————sides. Question. 84 Diagonals of a rectangle are————. Question. 85 A polygon having 10 sides is known as————. Question. 86 A rectangle whose adjacent sides are equal becomes a ————. Question. 87 If one diagonal of a rectangle is 6 cm long, length of the other diagonal is—–. Question. 88 Adjacent angles of a parallelogram are————. Question. 89 If only one diagonal of a quadrilateral bisects the other, then the quadrilateral is known as————. Question. 90 In trapezium ABCD with AB || CD, if \( \angle A\)= 100°, then \( \angle D\) =————. Question. 91 The polygon in which sum of all exterior angles is equal to the sum of interior angles is called————. True/False Question. 93 All squares are rectangles. Question. 94 All kites are squares. Question. 95 All rectangles are parallelograms. Question. 96 All rhombuses are square. Question. 97 Sum of all the angles of a quadrilateral is 180°. Question. 98 A quadrilateral has two diagonals. Question. 99 Triangle is a polygon whose sum of exterior angles is double the sum of interior angles. Question. 100 Solution. False Because it is not a simple closed curve as it intersects with itself more than once. Question. 101 A kite is not a convex quadrilateral. Question. 102 The sum of interior angles and the sum of exterior angles taken in an order are equal in case of quadrilaterals only. Question. 103 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. Question. 104 A polygon is regular, if all of its sides are equal. Question. 105 Rectangle is a regular quadrilateral. Question. 106 If diagonals of a quadrilateral are equal, it must be a rectangle. Question. 107 If opposite angles of a quadrilateral are equal, it must be a parallelogram. Question. 108 The interior angles of a triangle are in the ratio 1:2:3, then the ratio of its exterior angles is 3 : 2 : 1. Question. 109 Solution. False As it has 6 sides, therefore it is a concave hexagon. Question. 110 Diagonals of a rhombus are equal and perpendicular to each other. Question. 111 Diagonals of a rectangle are equal. Question. 112 Diagonals of rectangle bisect each other at right angles. Question. 113 Every kite is a parallelogram. Question. 114 Every trapezium is a parallelogram. Question. 115 Every parallelogram is a rectangle. Question. 116 Every trapezium is a rectangle. Question. 117 Every rectangle is a trapezium. Question. 118 Every square is a rhombus. Question. 119 Every square is a parallelogram. Question. 120 Every square is a trapezium. Question. 121 Every rhombus is a trapezium. Question. 122 A quadrilateral can be drawn if only measures of four sides are given. Question. 123 A quadrilateral can have all four angles as obtuse. Question. 124 A quadrilateral can be drawn, if all four sides and one diagonal is known. Question. 125 A quadrilateral can be drawn, when all the four angles and one side is given. Question. 126 A quadrilateral can be drawn, if all four sides and one angle is known. Question. 127 A quadrilateral can be drawn, if three sides and two diagonals are given. Question. 128 If diagonals of a quadrilateral bisect each other, it must be a parallelogram. Question. 129 A quadrilateral can be constructed uniquely, if three angles and any two included sides are given. Question. 130 A parallelogram can be constructed uniquely, if both diagonals and the angle between them is given. Question. 131 A rhombus can be constructed uniquely, if both diagonals are given. Question. 132 The diagonals of a rhombus are 8 cm and 15 cm. Find its side. Question. 133 Two adjacent angles of a parallelogram are in the ratio 1 : 3. Find its angles. Question. 134 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. Question. 135 In a rectangle ABCD, AB = 25 cm and BC = 15 cm. In what ratio, does the bisector of \(\angle C\) divide AB? Question. 136 PQRS is a rectangle. The perpendicular ST from S on PR divides \(\angle S\) in the ratio 2 : 3. Find \(\angle TPQ\). Question. 137 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? Question. 138 The adjacent angles of a parallelogram are (2x – 4)° and (3x – 1)°. Find the measures of all angles of the parallelogram. Question. 139 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? Question. 140 The ratio between exterior angle and interior angle of a regular polygon is 1 : 5. Find the number of sides of the polygon. Question. 141 Two sticks each of length 5 cm are crossing each other such that they bisect each other. What shape is formed by joining their end points? Give reason. Question. 142 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. Question. 143 A playground in the town is in the form of a kite. The perimeter is 106 m. If one of its sides is 23 m, what are the lengths of other three sides? Question. 144 In rectangle READ , find \(\angle EAR\), \(\angle RAD\) and \(\angle ROD\). Solution. Question. 145 In rectangle PAIR, find \(\angle ARI\), ZRMI and \(\angle PMA\). Solution. Question. 146 In parallelogram ABCD, find \(\angle B\), \(\angle C\) and \(\angle D\). Solution. Question. 147 In parallelogram PQRS, 0 is the mid-point of SQ. Find \(\angle S\), \(\angle R\), PQ, QR and diagonal PR. Solution. Question. 148 In rhombus BEAM, find \(\angle AME\) and \(\angle AEM\). Solution. Question. 149 In parallelogram FIST, find \(\angle SFT\), \(\angle OST\) and \(\angle STO\). Solution. Question. 150 In the given parallelogram YOUR, \(\angle RUO\)= 120° and 0Y is extended to points, such that \(\angle SRY\) = 50°. Find \(\angle YSR\). Solution. Question.151 In kite WEAR, \(\angle WEA\) = 70° and \(\angle ARW\) = 80°. Find the remaining two angles. Solution. Question.152 Solution. Question.153 In parallelogram LOST, SNLOL and \( SM\bot LT\). Find \(\angle STM\), \(\angle SON\) and \(\angle NSM\). Solution. Question. 154 In trapezium HARE, EP and RP are bisectors of \(\angle E\) and \(\angle R\), respectively. Find \(\angle HAR\) and \(\angle EHA\). Solution. Question. 155 In parallelogram MODE, the bisectors of \(\angle M\) and \(\angle O\) meet at Q. Find the measure of \(\angle MQO\). Question. 156 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. Solution. Question. 157 In the following figure of a ship, ABDH and CEFG are two parallelograms. Find the value of x. Solution. Question. 158 A rangoli has been drawn on the floor of a house. ABCD and PQRS both are in the shape of a rhombus. Find the radius of semi-circle drawn on each side of rhombus ABCD. Solution. Question. 159 ABCDE is a regular pentagon. The bisector of angle A meets the sides CD at M. Find \(\angle AMC\) Solution. Question. 160 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 = 24 x – 8. Question. 161 Find the values of x and y in the following parallelogram. Solution. Question. 162 Find the values of x and y in the following kite. Solution. Question. 164 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. Question. 165 In a quadrilateral PQRS, \(\angle P\) = 50°, \(\angle Q\) = 50°, \(\angle R\) = 60°. Find \(\angle S\). Is this quadrilateral convex or concave? Question. 166 Both the pairs of opposite angles of a quadrilateral are equal and supplementary. Find the measure of each angle. Question. 167 Find the measure of each angle of a regular octagon. Question. 168 Find the measure of an exterior angle of a regular pentagon and an exterior angle of a regular decagon. What is the ratio between these two angles? Question. 169 In the figure, find the value of x. Solution. Question. 170 Three angles of a quadrilateral are equal. Fourth angle is of measure 120°. What is the measure of equal angles? Question. 171 In a quadrilateral HOPE, PS and ES are bisectors of \(\angle P\) and \(\angle E\) respectively. Give reason. Question. 172 ABCD is a parallelogram. Find the values of x, y and z. Solution. Question. 173 Diagonals of a quadrilateral are perpendicular to each other. Is such a quadrilateral always a rhombus? Give a figure to justify your answer. Question. 174 ABCD is a trapezium such that AB || CD, \(\angle A\): \(\angle D\) = 2:1, \(\angle B\) : \(\angle C\) = 7:5. Find the angles of the trapezium. Question. 175 A line / is parallel to Line m and a-transversal p intersects them at X, Y respectively. Bisectors of interior angles at X and Y intersect at P and Q. Is PXQY a rectangle? Give reason. Question. 176 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. Question. 177 A diagonal of a parallelogram bisects an angle. Will it also bisect the other angle? Give reason. Question. 178 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. Question. 179 ABCD is a rhombus such that the perpendicular bisector of AB passes through D. Find the angles of the rhombus.[Hint Join BD. Then, AABD is equilateral.] Question. 180 ABCD is a parallelogram. Point P and Q are taken on the sides AB and AD, respectively and 4he parallelogram PRQA is formed. If \(\angle C\)= 45°, find \(\angle R\). Question. 181 In parallelogram ABCD, the angle bisector of \(\angle A\) bisects BC. Will angle bisector of B also bisect AD? Give reason. Question. 182 A regular pentagon ABCDE and a square ABFG are formed on opposite sides of AB. Find \(\angle BCF\)? Question. 183 Find maximum number of acute angles which a convex quadrilateral, a pentagon and a hexagon can have. Observe the pattern and generalise the result for any polygon. Question. 184 In the following figure, FD || BC || AE and AC || ED. Find the value of x. Solution. Question. 185 In the following figure, AB || DC and AD = BC. Find the value of x. Solution. Question. 186 Construct a trapezium ABCD in which AB || DC, \(\angle A\) = 105°, AD = 3 cm, AB = 4 cm and CD = 8 cm. Question. 187 Construct a parallelogram ABCD in which AB =4 cm, BC = 5cm and \(\angle B\) = 60°. Question. 188 Construct a rhombus whose side is 5 cm and one angle is of 60° Question. 189 Construct a rectangle whose one side is 3 cm and a diagonal is equal to 5 cm. Question. 190 Construct a square of side 4 cm. Question. 191 Construct a rhombus CLUE in which CL = 7.5 cm and LE = 6 cm. Question. 192 Construct a quadrilateral BEAR in which BE = 6 cm, EA = 7 cm, RB = RE = 5 cm and BA = 9 cm. Measure its fourth side. Question. 193 Construct a parallelogram POUR in which PO = 5.5 cm, OU = 7.2 cm and \(\angle O\) = 70°. Question. 194 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. Question. 195 Construct a parallelogram HOME with HO = 6 cm, HE = 4 cm and OE = 3 cm. Question. 196 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? Question. 197 Is it possible to construct a quadrilateral ROAM in which RO = 4 cm, OA = 5 cm, \(\angle O\) = 120°,\(\angle R\) = 105° and \(\angle A\) = 135°? If not, why? Question. 198 Construct a square in which each diagonal is 5 cm long. Question. 199 Construct a quadrilateral NEWS in which NE = 7 cm, EW = 6 cm, \(\angle N\) = 60°, \(\angle E\)= 110° and \(\angle S\) = 85° Question. 200 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. Question. 201 Find the measure of each angle of a regular polygon of 20 sides? Question. 202 Construct a trapezium RISK in which RI || KS, RI = 7 cm, IS = 5 cm, RK = 6.5 cm and \(\angle I\) = 60°. Question. 203 Construct a trapezium ABCD, where AB|| CD, AD = BC = 3.2 cm, AB = 6.4 cm and CD = 9.6 cm. Measure \(\angle B\) and \(\angle A\) [Hint Difference of two parallel sides gives an equilateral triangle.] Solution. NCERT Exemplar Class 8 Maths Solutions
NCERT Exemplar Solutions We hope the NCERT Exemplar Class 8 Maths Chapter 5 Understanding Quadrilaterals and Practical Geometry help you. If you have any query regarding NCERT Exemplar Class 8 Maths Chapter 5 Understanding Quadrilaterals and Practical Geometry, drop a comment below and we will get back to you at the earliest. What is true about angles that are supplementary to congruent angles?If two angles are congruent and supplementary, then each is a right angle. Same-Side Interior Angles Postulate: If a transversal intersects two parallel lines, then the same-side interior angles are supplementary.
What is the measure of angles that are both supplementary and congruent?Answer and Explanation: The only time that supplementary angles are congruent is when they both have a measure of 90°. Supplementary angles are defined as angles with measures that sum up to 180°.
Which is true for supplementary angles?The sum of two supplementary angles is always 180°.
Which is true about congruent angles?Congruent Angles have the same angle (in degrees or radians). That is all.
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