7th Class Mathematics The Triangle and its Properties Question Bank

done Geometry Total Questions - 40

• question_answer1)
  In the following figure, rays OA, OB, OC and OD are such that\[\angle \,\mathbf{AOB}\text{ }=\text{ }\mathbf{71}{}^\circ \], \[\angle \,\,\mathbf{BOC}\text{ }=\text{ }\mathbf{48}{}^\circ ,\text{ }\angle \text{ }\mathbf{COD}\text{ }=\text{ }\mathbf{X}{}^\circ \text{ }\mathbf{and}\text{ }\angle \text{ }\mathbf{DOA}\text{ }=\text{ }\mathbf{93}{}^\circ \]. What will be the value of \[x{}^\circ \].
  A)
  \[~136{}^\circ \] done clear
  B)
  \[~144{}^\circ \] done clear
  C)
  \[~148{}^\circ \] done clear
  D)
  \[~138{}^\circ \] done clear
  E)
   None of these done clear
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• question_answer2)
  In the shown figure, POQ. Is a straight line.      Based on above information, choose the one which is correct?
  A)
  \[a\text{ }=38{}^\circ \]            done clear
  B)
   \[\angle \,ROQ=96{}^\circ \,\] done clear
  C)
   \[\angle \,POR=84{}^\circ \] done clear
  D)
   \[\angle \,ROP-\angle \,ROQ=\text{ }12{}^\circ \] done clear
  E)
   None of these done clear
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• question_answer3)

  In the given figure, it is given that \[\mathbf{OA}\left| \text{ } \right|\text{ }\mathbf{EC}\]and\[\mathbf{OB}\left| \text{ } \right|\mathbf{ED}\].

  Based on above information, choose the one which is incorrect?

  A)
  \[\angle 1=\text{ }\angle 5\] done clear
  B)
   \[\angle 1=\text{ }\angle 3\] done clear
  C)
   \[\angle 1+\angle 2=180{}^\circ \] done clear
  D)
   \[\angle 2=\angle 5\] done clear
  E)
   None of these done clear
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• question_answer4)
  In the given figure, it is given that\[\mathbf{PQ}\left| \text{ } \right|\mathbf{RS}\], \[\angle \mathbf{QPM}\text{ }=\text{ }\mathbf{112}{}^\circ \] and\[\angle \text{ }\mathbf{MRS}\text{ }=\mathbf{124}{}^\circ \]. Find the value of\[\angle \text{ }\mathbf{PMR}\].
  A)
  \[~112{}^\circ \] done clear
  B)
   \[~124{}^\circ \] done clear
  C)
   \[~120{}^\circ \] done clear
  D)
   \[~128{}^\circ \] done clear
  E)
   None of these done clear
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• question_answer5)
  In the given figure PQRS is a quadrilateral such that \[\mathbf{PQ}\parallel \mathbf{RS}\]and\[\mathbf{SP}\parallel \mathbf{RQ}\]. If\[\angle \mathbf{QPS=88{}^\circ }\], then find the value of \[\angle \mathbf{SRQ}\]
  A)
  \[~92{}^\circ \] done clear
  B)
  \[~80{}^\circ \] done clear
  C)
  \[~68{}^\circ \]   done clear
  D)
   \[88{}^\circ \] done clear
  E)
  None of these done clear
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• question_answer6)
  In the given figure, \[\mathbf{p}\parallel \mathbf{q}\text{ }\mathbf{and}\text{ }\mathbf{r}\parallel \mathbf{s}\] and\[\angle \mathbf{sbp}=\mathbf{79}{}^\circ \]. Based on this information, which one among the following statements is correct?
  A)
  \[\angle 2=102{}^\circ \] done clear
  B)
  \[\text{ }\angle 3=79{}^\circ \] done clear
  C)
  \[\angle 4=100{}^\circ \] done clear
  D)
   All the above done clear
  E)
   None of these done clear
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• question_answer7)
  In a \[\Delta \,\,\mathbf{PQR}\], if\[\mathbf{2}\angle \mathbf{P}=\mathbf{18}\,\text{ }\angle \mathbf{Q}=\mathbf{9}\,\,\,\angle \mathbf{R}\], then _________.
  A)
  \[\angle P+\angle Q=150{}^\circ \] done clear
  B)
   \[\angle P-\angle Q-130{}^\circ \] done clear
  C)
  \[\angle R-\angle Q=20{}^\circ \] done clear
  D)
   All the above done clear
  E)
   None of these done clear
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• question_answer8)
  In the given figure, if \[\mathbf{MN}\parallel \text{ }\mathbf{QR}\] and \[\angle \mathbf{P=75{}^\circ }\], \[\angle \mathbf{Q = 60{}^\circ }\],  _________
  A)
  \[~\angle \,PMN=75{}^\circ \] done clear
  B)
   \[\angle \,NMQ=125{}^\circ \] done clear
  C)
   \[\angle \,PRQ=55{}^\circ \] done clear
  D)
   \[\angle \,MNR=135{}^\circ \] done clear
  E)
   None of these done clear
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• question_answer9)
  On producing a side of a triangle, the exterior angle so formed is \[128{}^\circ \]. If the interior opposite angles are in the ratio \[\mathbf{1}:\mathbf{3},\]then find the measure of the difference of greatest angle and the least angle of the triangle.
  A)
  \[35{}^\circ \] done clear
  B)
   \[58{}^\circ \] done clear
  C)
   \[23{}^\circ \]  done clear
  D)
   \[28{}^\circ \] done clear
  E)
   None of these done clear
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• question_answer10)
  If the sides of a triangle are produced in order, then the sum of exterior angles so formed will be _________.
  A)
  \[180{}^\circ \] done clear
  B)
   \[270{}^\circ \] done clear
  C)
   \[360{}^\circ \] done clear
  D)
   \[150{}^\circ \] done clear
  E)
   None of these done clear
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• question_answer11)
  Which among the following is not a Pythagorean triplets?
  A)
  (5, 12, 13) done clear
  B)
   (7, 24, 25) done clear
  C)
   (12, 35, 37) done clear
  D)
   (13, 12, 17) done clear
  E)
   None of these done clear
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• question_answer12)
  A 3.7 m long ladder is placed against a wall such that the foot of the ladder is 3.5m away from the wall. Find the height upto which the ladder reach the wall?
  A)
  1.6m  done clear
  B)
   1.8m done clear
  C)
   1.2m done clear
  D)
   3.2m done clear
  E)
   None of these done clear
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• question_answer13)
  Two poles of height 18m and 39m stand upright on a plane ground. If the distance between their feet is 28m. Find the distance between their tops.
  A)
  35m done clear
  B)
   37m done clear
  C)
   31m done clear
  D)
   39m done clear
  E)
   None of these done clear
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• question_answer14)
  A man goes 40m due east and then x m due north. If the is at a distance of 41m from his position, then find the value of x.
  A)
  6m done clear
  B)
   8m done clear
  C)
   9m done clear
  D)
  12m done clear
  E)
   None of these done clear
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• question_answer15)
  Which one among the following statements is incorrect?
  A)
  Two triangles are said to be congruent if pairs of corresponding sides and the corresponding angles are equal done clear
  B)
   Areas of two congruent figures are equal and if two figures have same area, they will be congruent. done clear
  C)
   The bisector of the vertical angle of an isosceles triangle bisects the base at right angles. done clear
  D)
   Two rectangles are congruent if they have same dimensions. done clear
  E)
   None of these done clear
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• question_answer16)
  Which one among the following is incorrect pair of the angle and its complement?
  A)
  \[67{}^\circ \text{ }\Leftrightarrow \text{ }23{}^\circ \] done clear
  B)
   \[45{}^\circ \text{ }\Leftrightarrow \text{ }45{}^\circ \] done clear
  C)
   \[34{}^\circ \text{ }\Leftrightarrow 46{}^\circ \] done clear
  D)
   \[42{}^\circ \text{ }\Leftrightarrow \text{ }48{}^\circ \] done clear
  E)
   None of these done clear
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• question_answer17)
  Which among the following is the angle which is triple of its supplement?
  A)
  \[135{}^\circ \] done clear
  B)
   \[120{}^\circ \] done clear
  C)
   \[150{}^\circ \] done clear
  D)
   \[110{}^\circ \] done clear
  E)
   None of these done clear
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• question_answer18)
  Which one among the following statements is true?
  A)
  A triangle cannot have more than one right angle. done clear
  B)
   A triangle cannot have more than one obtuse angle. done clear
  C)
   A triangle cannot have all the angles less than or greater than \[60{}^\circ \]. done clear
  D)
  All the above done clear
  E)
  None of these done clear
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• question_answer19)
  One of the acute of a right triangle is\[\mathbf{75{}^\circ }\]. Find the other acute angle.
  A)
  \[25{}^\circ \]  done clear
  B)
   \[35{}^\circ \] done clear
  C)
  \[45{}^\circ \] done clear
  D)
   \[15{}^\circ \] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer20)
  Which one among the following cannot be the length of sides of a right triangle?
  A)
  15cm, 20cm, 25cm done clear
  B)
   25cm, 65cm, 60cm done clear
  C)
   16cm, 30cm, 24cm done clear
  D)
   27cm, 45cm, 36cm done clear
  E)
   None of these done clear
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• question_answer21)
  In the shown figure, S and T are two points on equal sides PQ and PR of an isosceles triangle PQR such that PS = PT. If RS = 16cm then QT = ________.
  A)
  8cm done clear
  B)
   12cm done clear
  C)
  16cm    done clear
  D)
   20cm done clear
  E)
  None of these done clear
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• question_answer22)
  In a triangle the sides (in cm) are integers and the longest side is 3cm. Find the perimeter of the triangle considering that the triangle is not an equilateral triangle.
  A)
  6cm      done clear
  B)
   7cm done clear
  C)
  8cm      done clear
  D)
   9cm done clear
  E)
  None of these done clear
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• question_answer23)
  Which one of the following angles cannot be an interior angle of any convex polygon?
  A)
  \[90{}^\circ \]   done clear
  B)
   \[178{}^\circ \] done clear
  C)
  \[1{}^\circ \] done clear
  D)
   \[182{}^\circ \] done clear
  E)
  None of these done clear
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• question_answer24)
  Find the number of sides of the regular polygon whose each interior angle is \[\mathbf{128}\frac{\mathbf{4}}{\mathbf{7}}\]___________?
  A)
  9 done clear
  B)
   12 done clear
  C)
  7 done clear
  D)
   11 done clear
  E)
   None of these done clear
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• question_answer25)
  In the following figure, a hexagon is shown. Find the value of x.            
  A)
  \[100{}^\circ \] done clear
  B)
   \[89{}^\circ \] done clear
  C)
   \[99{}^\circ \]  done clear
  D)
   \[81{}^\circ \] done clear
  E)
   None of these done clear
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• question_answer26)
  The angles (in order) of a quadrilateral are in the ratio\[\mathbf{3}:\mathbf{4}:\mathbf{5}:\mathbf{6}\]. The quadrilateral is a _________.
  A)
  parallelogram done clear
  B)
   trapezium done clear
  C)
   kite      done clear
  D)
   rhombus done clear
  E)
   None of these done clear
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• question_answer27)
  In the given figure, PQR is an isosceles right triangle. Find the value of\[\mathbf{x}{}^\circ \].
  A)
  \[75{}^\circ \] done clear
  B)
   \[125{}^\circ \] done clear
  C)
   \[135{}^\circ \] done clear
  D)
   \[145{}^\circ \] done clear
  E)
   None of these done clear
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• question_answer28)
  In a regular polygon of n sides (where n < 10). How many such polygons are possible if each of its interior angles is obtuse angle?
  A)
  4  done clear
  B)
   5 done clear
  C)
   7         done clear
  D)
   6 done clear
  E)
   None of these done clear
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• question_answer29)
  In the figure shown, BC is produced to D. Find the value of\[\mathbf{x}\text{ }+\text{ }\mathbf{y}\].
  A)
  \[135{}^\circ \] done clear
  B)
   \[140{}^\circ \] done clear
  C)
   \[145{}^\circ \] done clear
  D)
   \[130{}^\circ \] done clear
  E)
   None of these done clear
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• question_answer30)
  The measure of angle P and thrice its supplement differ by \[\mathbf{20{}^\circ ,}\] then\[\angle \,\mathbf{P}\] can be _________.
  A)
  \[100{}^\circ \] done clear
  B)
   \[120{}^\circ \] done clear
  C)
   \[140{}^\circ \] done clear
  D)
   \[130{}^\circ \] done clear
  E)
   None of these done clear
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• question_answer31)
  Which one among the following cannot be the sides of a triangle?
  A)
  5cm, 7cm, 9cm done clear
  B)
   6cm, 5cm, 2cm done clear
  C)
   5cm, 8cm, 3cm done clear
  D)
   7cm, 10cm, 4cm done clear
  E)
   None of these done clear
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• question_answer32)
  In the shown figure, \[\mathbf{AB}\text{ }\left| \text{ } \right|\text{ }\mathbf{CD}\] and\[\angle \text{ }\mathbf{BGF}\text{ }=\text{ }\mathbf{90}{}^\circ \]. If\[\angle \text{ }\mathbf{EBG}\text{ }=\text{ }\mathbf{73}{}^\circ \], then find the value of\[\left( \mathbf{x}\text{ }+\text{ }\mathbf{y} \right){}^\circ \].
  A)
  \[42{}^\circ \] done clear
  B)
   \[34{}^\circ \] done clear
  C)
   \[46{}^\circ \] done clear
  D)
   \[36{}^\circ \] done clear
  E)
   None of these done clear
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• question_answer33)
  In the shown figure, three lines are intersecting at a point. If\[\mathbf{r=25{}^\circ }\,\,\mathbf{and}\,\,\mathbf{t{}^\circ =76{}^\circ }\], then find the value of P.
  A)
  \[79{}^\circ \]   done clear
  B)
   \[89{}^\circ \] done clear
  C)
   \[76{}^\circ \] done clear
  D)
   \[58{}^\circ \] done clear
  E)
   None of these done clear
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• question_answer34)
  In the shown figure,\[\angle \mathbf{ BAD= 2 }\angle \mathbf{ DAC}\]\[\angle \mathbf{B=}\,\angle \mathbf{C+48{}^\circ }\,\,\mathbf{and}\,\angle \,\mathbf{ADC=}\,\,\mathbf{132{}^\circ }\]. Find \[\angle \mathbf{BAC}\mathbf{.}\]
  A)
  \[99{}^\circ \] done clear
  B)
   \[120{}^\circ \] done clear
  C)
   \[108{}^\circ \] done clear
  D)
   \[126{}^\circ \] done clear
  E)
   None of these done clear
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• question_answer35)
  In the shown figure, PQRS is a square of side 12cm, and\[\mathbf{OM}\text{ }\bot \text{ }\mathbf{SR}\]. Find the length of MQ.
  A)
  \[4\sqrt{5}\,cm\] done clear
  B)
   \[6\sqrt{5}\,cm\] done clear
  C)
   \[3\sqrt{2}\,cm\] done clear
  D)
   \[6\sqrt{2}\,cm\] done clear
  E)
   None of these done clear
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• question_answer36)
  In\[\Delta \text{ }\mathbf{MNT}\text{ }\mathbf{and}\text{ }\Delta \text{ }\mathbf{PQR}\],\[\angle \text{ }\mathbf{N=}\text{ }\angle \text{ }\mathbf{Q = 90{}^\circ }\],\[\mathbf{MM}\,\,\mathbf{=}\,\,\mathbf{PQ}\,\,\mathbf{and}\,\,\mathbf{NT}\,\,\mathbf{=}\,\,\mathbf{QR}\] Which of the following property can be used to prove congruence of A MNT and A PQR?
  A)
  ASA      done clear
  B)
   SSS done clear
  C)
   SAS     done clear
  D)
   RHS done clear
  E)
   None of these done clear
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• question_answer37)
  In the figure shown below. \[\mathbf{2}\text{ }\angle \,\mathbf{A}\text{ }\mathbf{=}\angle \,\mathbf{BOC}\] OB and OC are bisector of \[\angle \]B and \[\angle \] C respectively. Find \[\angle \]A.
  A)
  \[50{}^\circ \] done clear
  B)
   \[75{}^\circ \] done clear
  C)
  \[60{}^\circ \]   done clear
  D)
   \[45{}^\circ \] done clear
  E)
  None of these done clear
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• question_answer38)
  In the figure shown, if\[\angle \,\mathbf{RQS}\text{ }\mathbf{=}\text{ }\angle \,\mathbf{PQS}\], \[\angle \,\mathbf{P}\text{ }\mathbf{=}\angle \,\mathbf{R+}\text{ }\mathbf{32}{}^\circ \] and\[\angle \mathbf{QSP=}\text{ }\mathbf{88}{}^\circ \], then find\[\angle \text{ }\mathbf{PQR}\].
  A)
  \[36{}^\circ \]   done clear
  B)
   \[42{}^\circ \] done clear
  C)
  \[48{}^\circ \] done clear
  D)
   \[49{}^\circ \] done clear
  E)
   None of these done clear
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• question_answer39)
  How many diagonals are there in a 60 sided convex plane?
  A)
  1580 done clear
  B)
   1710 done clear
  C)
  1810 done clear
  D)
   1680 done clear
  E)
  None of these done clear
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• question_answer40)
  If 10, 14 and m are sides of an acute angled triangle, then how many integer values of m are possible?
  A)
  5  done clear
  B)
   6 done clear
  C)
  7 done clear
  D)
   8 done clear
  E)
  None of these done clear
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