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Maths Assertion (A) & Reason (B) MCQ

Lines And Angles · CBSE STD 9 (CBSE - English Medium). 10 questions.

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Assertion (A) & Reason (B) MCQ

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10 questions · timed · auto-graded

MCQ 11 Mark
Statement-1 (A): In Fig., if $A B \| C D, \angle E A B=110^{\circ}$ and $\angle A E C=30^{\circ}$, then$\angle D C E=140^{\circ}$
Statement-2 (R): If two parallel lines are intersected by a tramsubersal, then each pair of alternate angles are equal.
Image
  • A
    Statement-1 and Statement-2 are true; Statement-2 is a correct explanation for Statement-4
  • ✓
    Statement-1 and Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement-1 is false, Statement-2 is true.
Answer
Correct option: B.
Statement-1 and Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(b)
Statement-2 is true. From E draw EF parallel to AB or CD. Now, $E F \| C D$ and CE is the transversal intersecting CD and EF at C and E respectively.
$\therefore \quad \angle C E F+\angle D C E=180^{\circ}$$\quad$$[\because$ Co-interior angles are supplementary $]$
$\Rightarrow \quad \angle C E F=180^{\circ}-\angle D C E$$\quad$...(i)
Again $A B \| E F$ and transversal AE cuts them at A and E respectively.
$\therefore \quad \angle B A E+\angle A E F=180^{\circ}$$\quad$$[\because$ Co-interior angles are supplementary $]$
$\Rightarrow \quad 110^{\circ}+30^{\circ}+\angle C E F=180^{\circ} \Rightarrow \angle C E F=40^{\circ}$$\quad$...(ii)
From (i) and (ii), we obtain
$40^{\circ}=180^{\circ}-\angle D C E \Rightarrow \angle D C E=180^{\circ}-40^{\circ}=140^{\circ}$
Thus, both the statements are true but statement-2 is not a correct explanation for statement-1. Hence, option (b) is correct.

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MCQ 21 Mark
Statement-1 (A): In Fig., if $B A\|E D, B C\| E F$ and $\angle A B C=180^{\circ}$, then $\angle D E F=100^{\circ}$
Statement-2 (R): If a transbersal iniersects two parallel lines, then each pair of cornsponding angles are equal and each pair of conseculive interion angles are supplementary.
Image
  • ✓
    Statement-1 and Statement-2 are true; Statement-2 is a correct explanation for Statement-3
  • B
    Statement-1 and Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement-1 is false, Statement-2 is true.
Answer
Correct option: A.
Statement-1 and Statement-2 are true; Statement-2 is a correct explanation for Statement-3
(a)
Statement-2 is true. Produce ED to meet BC at P.
Since $B A \| D E$ i.e. PE and transversal BC cuts them at B and P respectively. Therefore,
$\angle A B C=\angle E P C$$\quad$[Corresponding angles]
Since $B C \| E F$ and transversal PE meets them al P and E respectively. The sum of the interior angles on the same side of transversal are supplementary.
$\begin{array}{ll}
\therefore & \angle E P C+\angle P D F=180^{\circ} \\
\Rightarrow & \angle A B C+\angle D E F=180^{\circ} \\
\Rightarrow & 80^{\circ}+\angle D E F=180^{\circ} \Rightarrow \angle D E F=100^{\circ}\end{array}$
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MCQ 31 Mark
Statement-1 (A): In Fig., line lis paralld to liter m.
Statement-2 (R): If a transversal intersects two lines in such a way that a pair of consecutive interior angles are supplementary, then the two lines are parallel.
Image
  • A
    Statement-1 and Statement-2 are true; Statement-2 is a correct explanation for Statement-2
  • B
    Statement-1 and Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • ✓
    Statement-1 is false, Statement-2 is true.
Answer
Correct option: D.
Statement-1 is false, Statement-2 is true.
(d)
Statement-2 is true.
In Fig., we find that $82^{\circ}+97^{\circ}=179^{\circ} \neq 180^{\circ}$ i.e. pair of consecutive interior angles are not supplementary. Therefore, line l is not parallel to tine m.
Thus, statement-2 is true and statement-1 is not true. Hence, option (d) is correct.
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MCQ 41 Mark
Statement-1 (A): In fig., if $x=y$ and $a=b$, then line $I_1$ is parallel to linte $I_3$
Statement-2 (R): If a transvereral intersects two lines in such an way that a pair of corresponding angles are equal, then the two lines are parallel.
Image
  • ✓
    Statement-1 and Statement-2 are true; Statement-2 is a correct explanation for Statement-1
  • B
    Statement-1 and Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement-1 is false, Statement-2 is true.
Answer
Correct option: A.
Statement-1 and Statement-2 are true; Statement-2 is a correct explanation for Statement-1
(a)
Statement-2 is the corresponding angle axiom. So, it is true.
If $x=y$, then by using statement $-2, I_1 \| l_2$.$\quad$...(i)
If $a=b$, then by using statement $2, l_2 \| l_3$.$\quad$...(ii)
From (i) and (ii), we obtain $I_1 \| I_3$, So, statement- 1 is true. Thus, both the statements are true and statement-2 is a correct explanation for statement-1. Hence, option (a) is correct.

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MCQ 51 Mark
Statement-1 (A): In Fig. lines AB and CD intersect at O. IF $\angle A O C=40^{\circ}$, then $\angle B O C=140^{\circ}$
Statement-2 (R): If two lines intersect, then vertically opposite angles are equal.
Image
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-6
  • C
    Statement- 1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement- 2 is true.
Answer
Correct option: B.
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-6
b
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MCQ 61 Mark
Statement-1 (A): In Fig. if ACB is a straight line, then $\angle A C D=72^{\circ}$
Statement-2 (R): If a ray stands on a line, the sum of two adjacent angles formed is 180°.
Image
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-5
  • C
    Statement- 1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement- 2 is true.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
a
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MCQ 71 Mark
Statement-1 (A): In Fig. if AB || CD, $\angle A B E=130^{\circ}$ and $\angle E C D=110^{\circ}$, then $\angle B E C=60^{\circ}$.
Statement-2 (R): If a transversal intersects two parallel lines, then each pair of alternate angles are equal.
Image
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-4
  • C
    Statement- 1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement- 2 is true.
Answer
Correct option: B.
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-4
b
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MCQ 81 Mark
Statement-1 (A): In Fig. if PQ|| RS, then $\angle A C B=90^{\circ}$.
Statement-2 (R): If two parallel lines are intersected by a transversal, then each pair of alternate angles are equal.
Image
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-3
  • C
    Statement- 1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement- 2 is true.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
a
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MCQ 91 Mark
Statement-1 (A): In Fig 10.37, AB ||CD, $\angle B A O=60^{\circ}$ and $\angle O C D=110^{\circ}$, then $\angle A O C=50^{\circ}$.
Statement-2 (R): If two parallel lines are intersected by a transversal, then each pair of consecutive interior angles are equal.
Image
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-2
  • ✓
    Statement- 1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement- 2 is true.
Answer
Correct option: C.
Statement- 1 is true, Statement-2 is false.
c
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MCQ 101 Mark
Statement-1 (A): In Fig. if parallel lines I and m are intersected by a transversal 1, then x = 25
Statement-2 (R): If two parallel lines are intersected by a transversal, then each pair of consecutive interior angles are supplementary.
Image
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
  • C
    Statement- 1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement- 2 is true.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
a
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Assertion (A) & Reason (B) MCQ - Maths STD 9 Questions - Vidyadip