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

8th Grade > Mathematics

UNDERSTANDING QUADRILATERALS MCQs

Total Questions : 464 | Page 43 of 47 pages

Question 161
Find the values of x and y in the following parallelogram.

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Answer: Option A. ->
:
In a parallelogram, adjacent angles are supplementary.

∴ 120^{\circ} + (5 x + 10)^{\circ} = 180^{\circ} \Rightarrow 5 x + 10^{\circ} + 120^{\circ} = 180^{\circ} \Rightarrow 5 x = 180^{\circ} - 130^{\circ} \Rightarrow 5 x = 50^{\circ} \Rightarrow x = 10^{\circ}

Also, opposite angles are equal in a parallelogram.
Therefore,

6 y = 120^{\circ} \Rightarrow y = 20^{\circ}

Question 422.

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 = 24x - 8.

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Answer: Option A. ->
:
Given, EFGH is a rectangle in which diagonals are intersecting at the point J.

Question 160Quadrilateral EFGH Is A Rectangle In Which J Is ...

We know that the diagonals of a rectangle bisect each other and are equal.
Then, EG

= 2 \times J F

\Rightarrow 24 x - 8 = 2 (8 x + 4) \Rightarrow 24 x - 8 = 16 x + 8 \Rightarrow 24 x - 16 x = 8 + 8 \Rightarrow 8 x = 16 \Rightarrow x = 2

Question 423.

Question 162
Find the values of x and y in the following kite.

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Answer: Option A. ->
:
The given figure is a kite.
In a kite, one pair of opposite angles are equal.

∴ y = 110^{\circ}

Now, by the angle sum property of a quadrilateral, we have

110^{\circ} + 60^{\circ} + 110^{\circ} + x = 360^{\circ} \Rightarrow x = 360^{\circ} - 280^{\circ} \Rightarrow x = 80^{\circ}

Question 424.

Question 163
Find the value of x in the trapezium ABCD given below

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Answer: Option A. ->
:
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 425.

Question 164
Two angles of a quadrilateral are each of measure $75^{\circ}$ and the other two angles are equal. What is the measure of these two angles? Name the possible figures so formed.

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Answer: Option A. ->
:
Let ABCD be a quadrilateral,
where

∠ A = ∠ C = 75^{\circ}

and

∠ B = ∠ D = x

[say]

Question 164Two Angles Of A Quadrilateral Are Each Of Measur...

Then, by the angle sum property of a quadrilateral, we have

∠ A + ∠ B + ∠ C + ∠ D = 360^{\circ} \Rightarrow 75^{\circ} + x + 75^{\circ} + x = 360^{\circ} \Rightarrow 2 x = 360^{\circ} - 150^{\circ} \Rightarrow 2 x = 210^{\circ} \Rightarrow x = 105^{\circ}

Thus, other two angles are of

105^{\circ}

each.
Since, opposite angles are equal, therefore the quadrilateral is a parallelogram.

Question 426.

Question 165
In a quadrilateral PQRS, $∠ P = 50^{\circ}, ∠ Q = 50^{\circ}, ∠ R = 60^{\circ}$ . Find $∠ S$ . Is this quadrilateral convex or concave?

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Answer: Option A. ->
:
Given a quadrilateral PQRS, where

∠ P = 50^{\circ}, ∠ Q = 50^{\circ}

and

∠ R = 60^{\circ}

Now, by the angle sum property of a quadrilateral, we have

∠ P + ∠ Q + ∠ R + ∠ S = 360^{\circ} \Rightarrow 50^{\circ} + 50^{\circ} + 60^{\circ} + ∠ S = 360^{\circ} \Rightarrow ∠ S = 360^{\circ} - 160^{\circ} \Rightarrow ∠ S = 200^{\circ}

One interior angle of the given quadrilateral is greater than

180^{\circ}

, therefore the quadrilateral is concave.

Question 427.

Question 166
Both the pairs of opposite angles of a quadrilateral are equal and supplementary. Find the measure of each angle.

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Answer: Option A. ->
:
Let ABCD be a quadrilateral, such that

∠ A = ∠ C, ∠ B = ∠ D

and also

∠ A + ∠ C = 180^{\circ}, ∠ B + ∠ D = 180^{\circ}

Now,

∠ A + ∠ A = 180^{\circ}

[

∵ ∠ C = ∠ A

]

\Rightarrow 2 ∠ A = 180^{\circ} \Rightarrow ∠ A = 90^{\circ} S i m i l a r l y, ∠ B = 90^{\circ}

Hence, each angle is a right angle.

Question 428.

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?

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Answer: Option A. ->
:
We know that, a pentagon has 5 sides and a decagon has 10.
Measure of each exterior angle of a regular pentagon