Understanding Quadrilaterals(8th Grade > Mathematics ) Questions and answers for exam Preparation

8th Grade > Mathematics

UNDERSTANDING QUADRILATERALS MCQs

Total Questions : 464 | Page 6 of 47 pages

Question 51.
Find the value of x in the trapezium ABCD given below

Discuss Question

:
Given, a trapezium ABCD in which

∠ A = (x - 20)^{\circ}, ∠ D = (x + 40)^{\circ}

Since, in a trapezium, the angles between the parallel lines are supplementary,

(x - 20) + (x + 40) = 180^{\circ} \Rightarrow x - 20 + x + 40 = 180^{\circ} \Rightarrow 2 x + 20^{\circ} = 180^{\circ} \Rightarrow 2 x = (180^{\circ} - 20^{\circ}) = 160^{\circ} \Rightarrow x = 80^{\circ}

Question 52.
A quadrilateral whose opposite sides and all the angles are equal is a
a) Rectangle
b) Parallelogram
c) Square
d) Rhombus

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:
We know that in a rectangle, opposite sides and all the angles are equal.

Question 53. In a concave polygon, no part of any of their diagonals is external.

True
False
Pentagon
Can't be determined

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Answer: Option B. -> False
:
B
A concave polygon will have some part of at least one diagonal external.

Question 54. Which of the following is true?

All squares are rectangles
All rectangles are squares
All rectangles are rhombuses
None of the above

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Answer: Option A. -> All squares are rectangles
:
A
The statement that all squares are rectangles is true because a square is a special type of rectangle where, the adjacent sides are equal.

Question 55. Which among the following has the most number of diagonals?

Triangle
Quadrilateral
Pentagon
Can't be determined

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Answer: Option C. -> Pentagon
:
C
The pentagon has the most number of vertices among the options. Hence, it has themost number of diagonals.

Question 56. Which of the following is not a model for a plane surface?

Top surface of table
Surface of paper
Body of car
None of these

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Answer: Option C. -> Body of car
:
C
The body of a car is a 3 dimensional surface. It is not a plane 2 dimensional surface

Question 57. In the given diagram, the value of x is ___ degrees.

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:
In quadrilateral ABCD,

∴ ∠ A B C + ∠ B C D + ∠ C D A + ∠ D A B = 360^{\circ} 40^{\circ} + 50^{\circ} + ∠ C D A + 70^{\circ} = 360^{\circ} \Rightarrow ∠ C D A + 160^{\circ} = 360^{\circ} \Rightarrow ∠ C D A = 360^{\circ} - 160^{\circ} = 200^{\circ}

Now,

∠ C D A + ∠ A D C = 360^{\circ} (∵

Angle at a point)

200^{\circ} + x = 360^{\circ} \Rightarrow x = 360^{\circ} - 200^{\circ} \Rightarrow x = 160^{\circ}

Question 58. In parallelogram ABCD, which of the two angles are equal?

Angles A & B
Angles B & C
Angles A & C
Angles C & D

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Answer: Option C. -> Angles A & C
:
C

In Parallelogram ABCD, Which Of The Two angles Are Equal?

In a parallelogram, the two opposite angles are equal. Hence, if the four vertices of a parallelogram are A, B, C, D in cyclic order, then

∠ A & ∠ C

and

∠ B & ∠ D

are equal.

Question 59. Consider the figure shown. What type of quadrilateral can it be?

Rhombus
Parallelogram
Kite
Triangle

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Answer: Option B. -> Parallelogram
:
B
In the given figure thepair of opposite sides are parallel and equal. So, the given figure is a parallelogram.
Among the options, the quadrilateral ABCD can be either'Rhombus' or'Parallelogram'. [

∵

Rhombus is also a parallelogram]
But adajcent sides of ABCD are not equal (ie, AD and CD are not equal).
So, ABCD cannot bea rhombus. Hence, ABCD is a paralleogram.

Question 60. The sum of exterior angles of a polygon (in degrees) with 10 sides is
___.

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:
The sum of all exterior angles of a polygon, irrespective of the number of its sides, is equal to