8th Class Mathematics Understanding Quadrilaterals Question Bank

done Quadrilaterals Total Questions - 40

• question_answer1)
  The angles of quadrilateral are in the ratio 2 : 3 : 5 : 8. The smallest angle is
  A)
   \[60{}^\circ \]                          done clear
  B)
   \[40{}^\circ \]  done clear
  C)
   \[{{20}^{{}^\circ }}\]                                    done clear
  D)
   \[{{50}^{{}^\circ }}\] done clear
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• question_answer2)
  In a parallelogram ABCD, if \[\angle \mathbf{A}=\mathbf{4}\angle \mathbf{B}\], then \[\angle \mathbf{A}+\angle \mathbf{C}\]
  A)
   \[{{260}^{{}^\circ }}\]                       done clear
  B)
   \[{{150}^{{}^\circ }}\]             done clear
  C)
   \[{{140}^{{}^\circ }}\]                       done clear
  D)
   \[{{288}^{{}^\circ }}\] done clear
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• question_answer3)
  In a quadrilateral PQRS, \[\angle \mathbf{P}:\angle \mathbf{Q}:\angle \mathbf{R}:\angle \mathbf{S}=\mathbf{2}:\mathbf{3}:\mathbf{3}:\mathbf{2}.\]Then  QRS is a ______
  A)
   Parallelogram                  done clear
  B)
  Isosceles trapezium done clear
  C)
   Rectangle          done clear
  D)
   square done clear
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• question_answer4)
  BEST is a rhombus in which \[\angle \mathbf{T}=\mathbf{12}{{\mathbf{0}}^{{}^\circ }}\]and \[TE=6cm.\]The perimeter of the rhombus is ___cm
  A)
   24cm     done clear
  B)
   12cm           done clear
  C)
   18cm                           done clear
  D)
   30cm done clear
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• question_answer5)
  A rectangle in which the diagonals are perpendicular is called a _____
  A)
   Rhombus done clear
  B)
   Square done clear
  C)
   Both A & B                  done clear
  D)
   None of these done clear
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• question_answer6)
  The angles of a quadrilateral are in the ratio 6 : 7 : 8 : 9, then which of the following can be concluded?
  A)
   Exactly two angles are obtuse done clear
  B)
   Two pairs of angles are supplementary done clear
  C)
   Both A & B done clear
  D)
   None of these done clear
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• question_answer7)
  In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1:2:3:4, Then the measure of each angles of the quadrilateral is
  A)
   \[{{36}^{{}^\circ }},{{72}^{{}^\circ }},{{108}^{{}^\circ }},{{144}^{{}^\circ }}\]          done clear
  B)
   \[{{45}^{{}^\circ }},{{110}^{{}^\circ }},{{55}^{{}^\circ }},{{150}^{{}^\circ }}\] done clear
  C)
   \[{{15}^{{}^\circ }},{{130}^{{}^\circ }},{{45}^{{}^\circ }},{{150}^{{}^\circ }}\]                      done clear
  D)
   none of these done clear
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• question_answer8)
  Sides BA and DC of a quadrilateral ABCD are produced as shown in figure, then \[\angle \mathbf{a}+\angle \mathbf{b}\] is equal to
  A)
   \[\angle x-\angle y\]                    done clear
  B)
   \[\angle x+\angle y\] done clear
  C)
   \[\angle x+\angle 2y\]                 done clear
  D)
   none of these done clear
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• question_answer9)
  The ratio of two sides of a parallelogram is as 3 : 5, and its perimeter is 48 m, then the sides of the parallelogram is
  A)
   9 m, 15 m      done clear
  B)
   3 m, 5 m done clear
  C)
   33 m, 25 m                   done clear
  D)
   none of these done clear
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• question_answer10)
  The opposite angles of a parallelogram are \[{{\left( \mathbf{3x}+\mathbf{5} \right)}^{{}^\circ }}\]and\[{{\left( \mathbf{61}-\mathbf{x} \right)}^{{}^\circ }}\]. Find the measure of four angles.
  A)
   \[{{47}^{{}^\circ }},{{133}^{{}^\circ }},{{47}^{{}^\circ }},{{133}^{{}^\circ }}\] done clear
  B)
   \[{{80}^{{}^\circ }},{{100}^{{}^\circ }},{{80}^{{}^\circ }},{{100}^{{}^\circ }}\] done clear
  C)
   \[{{77}^{{}^\circ }},{{103}^{{}^\circ }},{{77}^{{}^\circ }},{{103}^{{}^\circ }}\]          done clear
  D)
   \[{{94}^{{}^\circ }},{{86}^{{}^\circ }},{{94}^{{}^\circ }},{{86}^{{}^\circ }}\] done clear
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• question_answer11)
  In figure, ABCD is \[\parallel \mathbf{gm}\] with \[\angle \mathbf{A}=\mathbf{8}{{\mathbf{0}}^{{}^\circ }},\]the internal bisectors of \[\angle \mathbf{B}\] and \[\angle \mathbf{C}\] meet at 0. Find the measure of three angles of ABCO
  A)
   \[{{30}^{{}^\circ }},{{60}^{{}^\circ }},{{90}^{{}^\circ }}\]                     done clear
  B)
   \[{{40}^{{}^\circ }},{{50}^{{}^\circ }},{{90}^{{}^\circ }}\] done clear
  C)
   \[{{60}^{{}^\circ }},{{60}^{{}^\circ }},{{60}^{{}^\circ }}\]                     done clear
  D)
   \[{{70}^{{}^\circ }},{{50}^{{}^\circ }},{{60}^{{}^\circ }}\] done clear
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• question_answer12)
  Find the measure of all angles of a parallelogram whose consecutive angles are in the ratio 1 : 3.
  A)
   \[{{60}^{{}^\circ }},{{120}^{{}^\circ }},{{60}^{{}^\circ }},{{120}^{{}^\circ }}\]  done clear
  B)
   \[{{85}^{{}^\circ }},{{95}^{{}^\circ }},{{85}^{{}^\circ }},{{95}^{{}^\circ }}\] done clear
  C)
   \[{{50}^{{}^\circ }},{{130}^{{}^\circ }},{{50}^{{}^\circ }},{{130}^{{}^\circ }}\]          done clear
  D)
  \[{{45}^{{}^\circ }},{{135}^{{}^\circ }},{{45}^{{}^\circ }},{{135}^{{}^\circ }}\] done clear
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• question_answer13)
  A diagonal and a side of a rhombus are of equal length. Find the measure of the angles of the rhombus.
  A)
   \[{{60}^{{}^\circ }},{{120}^{{}^\circ }},{{60}^{{}^\circ }},{{120}^{{}^\circ }}\]     done clear
  B)
   \[{{45}^{{}^\circ }},{{45}^{{}^\circ }},{{135}^{{}^\circ }},{{135}^{{}^\circ }}\] done clear
  C)
   \[{{85}^{{}^\circ }},{{95}^{{}^\circ }},{{85}^{{}^\circ }},{{95}^{{}^\circ }}\]                         done clear
  D)
   \[{{80}^{{}^\circ }},{{100}^{{}^\circ }},{{80}^{{}^\circ }},{{100}^{{}^\circ }}\] done clear
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• question_answer14)
  For which of the following, diagonals bisect each other?
  A)
   Square     done clear
  B)
   Kite done clear
  C)
   Trapezium                     done clear
  D)
   Quadrilateral done clear
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• question_answer15)
  If \[\mathbf{x}=\mathbf{y}\], then find the value of x in the trapezium ABCD given below
  A)
  \[60{}^\circ \]                           done clear
  B)
  \[70{}^\circ \] done clear
  C)
  \[80{}^\circ \] done clear
  D)
  \[100{}^\circ \] done clear
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• question_answer16)
  A quadrilateral whose opposite sides and all the angles are equal is a
  A)
   Rectangle      done clear
  B)
   Parallelogram done clear
  C)
   Kite                              done clear
  D)
   Rhombus done clear
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• question_answer17)
  What is the maximum number of obtuse angles that a quadrilateral can have?
  A)
   1                                 done clear
  B)
   2               done clear
  C)
   3 done clear
  D)
   4 done clear
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• question_answer18)
  In the trapezium ABCD, the measure of \[\angle \mathbf{D}\] is
  A)
   \[{{55}^{{}^\circ }}\]                                    done clear
  B)
   \[{{115}^{{}^\circ }}\]            done clear
  C)
   \[{{135}^{{}^\circ }}\]                                   done clear
  D)
   \[{{125}^{{}^\circ }}\] done clear
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• question_answer19)
  If PQRS is a parallelogram, then \[\angle \mathbf{P}-\angle R\] is equal to
  A)
   \[{{60}^{{}^\circ }}\]                        done clear
  B)
   \[~{{90}^{{}^\circ }}\]             done clear
  C)
   \[{{80}^{{}^\circ }}\]                                    done clear
  D)
   \[{{0}^{{}^\circ }}\] done clear
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• question_answer20)
  PQRS is a square, PR and SQ intersect at O. Then \[\angle \mathbf{POQ}\] is a
  A)
   Right angle  done clear
  B)
   Straight line done clear
  C)
   Reflex angle                  done clear
  D)
   Complete angle done clear
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• question_answer21)
  Adjacent sides of a rectangle are in the ratio 5 : 12, if the perimeter of the rectangle is 34 cm, find the length of the diagonal.
  A)
   13 cm   done clear
  B)
   12cm          done clear
  C)
   25 cm                          done clear
  D)
   5 cm done clear
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• question_answer22)
  All the sides of a regular polygon are
  A)
   Parallel     done clear
  B)
   Equal in length done clear
  C)
   Not parallel                   done clear
  D)
   Not equal done clear
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• question_answer23)
  A parallelogram each of whose angles measures \[\mathbf{90}{}^\circ \]is
  A)
   Rectangle   done clear
  B)
   Rhombus done clear
  C)
   Kite                              done clear
  D)
   Trapezium done clear
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• question_answer24)
  Diagonals of a rectangle are: -
  A)
   equal to each other          done clear
  B)
   not equal done clear
  C)
   one is double of the other                done clear
  D)
   none of these done clear
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• question_answer25)
  Diagonals of a parallelogram ____ each other.
  A)
   bisect      done clear
  B)
   equal to done clear
  C)
   perpendicular to        done clear
  D)
   none of these done clear
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• question_answer26)
  Find the angle measure x in the figure.
  A)
   \[{{150}^{{}^\circ }}\]                       done clear
  B)
   \[{{140}^{{}^\circ }}\]    done clear
  C)
   \[{{130}^{{}^\circ }}\]                                   done clear
  D)
   \[{{160}^{{}^\circ }}\] done clear
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• question_answer27)
  Find the angle measure x in the figure.
  A)
   \[{{80}^{{}^\circ }}\]                                    done clear
  B)
   \[{{90}^{{}^\circ }}\]             done clear
  C)
   \[{{110}^{{}^\circ }}\]  done clear
  D)
   \[{{160}^{{}^\circ }}\] done clear
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• question_answer28)
  In fig. BEST is a parallelogram. Find the value x, y and z
  A)
   \[{{100}^{{}^\circ }},{{90}^{{}^\circ }},{{70}^{{}^\circ }}\]                   done clear
  B)
   \[{{90}^{{}^\circ }},{{60}^{{}^\circ }},{{70}^{{}^\circ }}\] done clear
  C)
   \[{{60}^{{}^\circ }},{{110}^{{}^\circ }},{{70}^{{}^\circ }}\]                   done clear
  D)
   \[{{100}^{{}^\circ }},{{100}^{{}^\circ }},{{80}^{{}^\circ }}\] done clear
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• question_answer29)
  RENT is a rectangle. Its diagonals meet at O. Find x. If \[\mathbf{OR}=\mathbf{2x}+\mathbf{4}\]and \[\mathbf{OT}=\mathbf{3x}+\mathbf{l}\]
  A)
   3 done clear
  B)
   4         done clear
  C)
   5                                 done clear
  D)
   6 done clear
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• question_answer30)
  In figure, abcd is a quadrilateral in which \[AB\parallel CD\] find x and y.
  A)
   \[{{100}^{{}^\circ }},{{60}^{{}^\circ }}\]   done clear
  B)
   \[{{90}^{{}^\circ }},{{50}^{{}^\circ }}\] done clear
  C)
   \[{{110}^{{}^\circ }},{{70}^{{}^\circ }}\]                done clear
  D)
   \[{{120}^{{}^\circ }},{{60}^{{}^\circ }}\] done clear
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• question_answer31)
  ABCD is a cyclic quadrilateral and 0 is the centre of the circle If \[\angle COD={{120}^{{}^\circ }}\]and \[\angle \mathbf{BAC}=\mathbf{6}{{\mathbf{0}}^{{}^\circ }}\], then the value of \[\angle \mathbf{BCD}\] is equal to
  A)
   \[{{70}^{{}^\circ }}\]                        done clear
  B)
   \[{{90}^{{}^\circ }}\]             done clear
  C)
   \[{{60}^{{}^\circ }}\]    done clear
  D)
   \[{{80}^{{}^\circ }}\] done clear
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• question_answer32)
  PQRS is a trapezium in which \[\mathbf{PS}\parallel \mathbf{QR}\] and \[\mathbf{PQ}=\mathbf{SR}=\mathbf{12}\]m, then the distance of PS from QR is:
  A)
   \[10\sqrt{2}m\]                          done clear
  B)
   \[4\sqrt{2}m\]        done clear
  C)
   \[5\sqrt{2}m\]                           done clear
  D)
   \[6\sqrt{2}m\] done clear
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• question_answer33)
  The sides QP and SR of quadrilateral PQRS are produced as shown in figure Also, \[(\mathbf{PQ}\parallel \mathbf{SR})\]. Then which of the following statements is correct?
  A)
   \[2{{x}^{{}^\circ }}+{{y}^{{}^\circ }}={{a}^{{}^\circ }}+{{b}^{{}^\circ }}\]             done clear
  B)
   \[{{x}^{{}^\circ }}+\frac{1}{2}{{y}^{{}^\circ }}=\frac{{{a}^{{}^\circ }}+{{b}^{{}^\circ }}}{2}\] done clear
  C)
   \[{{x}^{{}^\circ }}+{{y}^{{}^\circ }}={{a}^{{}^\circ }}+{{b}^{{}^\circ }}\]      done clear
  D)
   \[{{x}^{{}^\circ }}+{{a}^{{}^\circ }}={{y}^{{}^\circ }}+{{b}^{{}^\circ }}\] done clear
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• question_answer34)
  If ABCD is a quadrilateral whose diagonals AC and BD intersect at 0, then:
  A)
   \[\left( AB+BC+CD+DA \right)<\left( AC+BD \right)\] done clear
  B)
   \[\left( AB+BC+CD+DA \right)>2\left( AC+BD \right)\] done clear
  C)
   \[\left( AB+BC+CD+DA \right)>\left( AC+BD \right)\] done clear
  D)
   \[AB+BC+CD+DA-2\left( AC+BD \right)\] done clear
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• question_answer35)
  In the adjoining figure, ABCD is a quadrilateral in which AB is the longest side and CD is the shortest side, then:
  A)
   \[\angle C>\angle A\,and\,\angle D>\angle B\]     done clear
  B)
   \[\angle C>\angle A\,and\,\angle B>\angle D\] done clear
  C)
   \[\angle C<\angle A\,and\,\angle D<\angle B\]             done clear
  D)
   \[\angle C<\angle A\,and\,\angle D=\angle B\] done clear
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• question_answer36)
  In the given figure, ABCD is a square. A line segment DX cuts the side BC at X and the diagonal AC at O Such that \[\angle \mathbf{COD}=\mathbf{11}{{\mathbf{5}}^{{}^\circ }}\]and \[\angle \mathbf{OXC}={{\mathbf{x}}^{{}^\circ }}\]. The value of x is:
  A)
   \[{{40}^{{}^\circ }}\]                         done clear
  B)
   \[{{70}^{{}^\circ }}\] done clear
  C)
   \[{{80}^{^{{}^\circ }}}\]                              done clear
  D)
   \[{{85}^{{}^\circ }}\] done clear
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• question_answer37)
  In the given figure \[\mathbf{AE}=\mathbf{BC}\] and \[\mathbf{AE}\parallel \mathbf{BC}\] and the three sides AB, CD and ED are  equal in length. If \[\angle \mathbf{A}=\mathbf{10}{{\mathbf{5}}^{{}^\circ }}\], find measures of \[\angle \mathbf{BCD}:\]
  A)
   \[{{138}^{{}^\circ }}\]                                   done clear
  B)
   \[{{165}^{{}^\circ }}\] done clear
  C)
   \[{{88}^{{}^\circ }}\]                        done clear
  D)
   None of these done clear
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• question_answer38)
  A point X inside a rectangle PQRS is joined to the vertices then, which of the following is true?
  A)
   area\[\left( \Delta PSX \right)=area\left( \Delta PXQ \right)\] done clear
  B)
   area\[\left( \Delta PSX \right)\]+area\[\left( \Delta PXQ \right)\]=area(RSX) area\[\left( \Delta RQX \right)\] done clear
  C)
   area\[\left( \Delta PXS \right)\]+area\[\left( \Delta RXQ \right)\]=area\[\left( \Delta SRX \right)\] +area\[\left( \Delta PXQ \right)\] done clear
  D)
   None of these done clear
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• question_answer39)
  In the adjoining figure, the value of x and y are: (If ABCD is parallelogram)
  A)
   \[{{5}^{{}^\circ }},{{4}^{{}^\circ }}\] done clear
  B)
   \[{{3}^{{}^\circ }},{{4}^{{}^\circ }}\]         done clear
  C)
   \[{{2}^{{}^\circ }},{{1}^{{}^\circ }}\]                    done clear
  D)
   None of these done clear
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• question_answer40)
  In the adjoining figure, ABCD is a parallelogram and E, F are the centroids of \[\Delta \mathbf{ABC}\] and \[\Delta \mathbf{ACD}\] respectively, then EF equals:
  A)
   AE       done clear
  B)
   BE       done clear
  C)
   CE                               done clear
  D)
   DE done clear
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