Understanding quadrilaterals class 8 worksheets with Answers
In this page we have Understanding quadrilaterals class 8 worksheets with Answers.This worksheet includes Multiple choice question , fill in the blank,True and false, Long answer type questions. Hope you like them and do not forget to like , social share
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Long Answer Type
Question 1.
Find the number of sides of a regular polygon in which each exterior angle has a measure of 40°$
Answer
exterior angle=40°
Interior angle =180 -40=140 °
Let n be the sides, then
Sum of interior angles= $(n-2) \times 180$
$140 n=(n-2) \times 180$
$n=9$
Question 2.
The perimeter of the parallelogram is 38 cm . One of the side is 12 cm, find the other side
Answer
In a parallelogram, oppossite sides are equal
Let x be the other side
Then
$2x + 2 \times 12 =38$
$x=7$ cm
Question 3.
Diagonals of the rhombus is 10 cm and 16 cm . What is the area of the rhombus
Answer
Area of the rhombus = $ \frac {1}{2} \times d_1 \times d_2$
Where $d_1$ and $d_2$ are the diagonals
Now as per the question
Question 4.
One of the angle in the parallelogram is 50°. Find the other angles in the parallelogram
Answer
Adjacent angles are supplementary, So
$x + 50=180$
x=130°
So angles are 50°,130°,50°, 130°
Question 5.
In the below figure, the measure of the angle DBC
Answer
In triangle PAB
$\angle APB + 31 + 29=180$
$\angle APB=120^0$
So $\angle BPC= 180 -120=60^0$
In triangle BPC
$\angle DBC + 60 + 34=86^0$
$\angle =
Question 6.
Three angles of a quadrilateral are 50°, 40° and 123°.Find its fourth angle.
Answer
Let fourth angle be x. Then $50 + 40 + 123 + x = 360$.
or $x = 360 – 50 – 40 – 123$
$= 360 – 213 = 147$
Question 7.
In the figure, HOPE is a rectangle. Its diagonals meet at G. If HG = 5x + 1 and EG = 4x + 19, find x
Answer
Since diagonals of a rectangle bisect each other,
HP = 2HG = 2 (5x + 1) = 10x +2
and OE = 2EG = 2(4x +19) = 8x + 38
Diagonals of a rectangle are equal. So HP = OE
or 10x + 2 = 8x + 38
or 2x = 36 or x = 18
Question 8.
In the given parallelogram YOUR, $\angle RUO = 120^0$ and OY is extended to point S such that $\angle SRY = 50^0$. Find $\angle YSR$
Answer
Since in parallelogram, opposite angles are equal
$\angle RYO=120^0$
Then $\angle RYS=180 -120=60^0$
Now in a triangle RYS
$\angle YSR + \angle RYS + \angle YRS=180$
$\angle YSR= 180- 60-50=70^0$
Question 9.
The diagonals of a rhombus are 8 cm and 6 cm. Find its side.
Answer
Since diagonals bisect each other and are Perpendicular,Side is given by pythagorus theorem as
$a= \frac {1}{2} \sqrt {d_1^2 + d_2^2} = 5$ cm
Question 10.
Two angles of a quadrilateral are each of measure 75° and the other two angles are equal. What is the measure of these two angles
Answer
So $2 \times 75 + 2x=360
$x=105$
Fill in the Blank
Question 11.
(i) Diagonals of a rectangle are __________.
(ii)In an parallegram, adjacents angles are _____
(iii)The sum of all exterior angles of a polygon is __________.
(iv)The measure of each exterior angle of a regular pentagon is __________.
(v) The number of sides of a regular polygon whose each interior angle is of 135° is ___
Answer
(i) equal
(ii)equal
(iii) 360°
(iv) 72°
(v) 8
True and False
Question 12.
(i) Diagonals of a rectangle are perpendicular to each other
(ii)All angles of a trapezium are equal
(iii)Every square is a trapezium.
(iv)If diagonals of a quadrilateral are equal, it must be a rectangle.
(v) Every square is a rhombus
(vi) ALl parallelograms are kites but all kites are not parallelogram
Question 13.
The sum of angles of a concave quadrilateral is
(a) more than 360°
(b) less than 360°
(c) equal to 360°
(d) twice of 360° Question 14.
The sum of adjacent angles of a parallelogram is
(a) 180°
(b) 120°
(c) 360°
(d) 90° Question 15.
ABCD is a rectangle .F and E are the mid points of BC and CD respectively. If area of the $\Delta BEF=7cm^2$, then the area of the rectangle ABCD is
(a) 49 cm2
(b) 42 cm2
(c) 56 cm2
(d) 28 cm2 Question 16.
Length of one of the diagonals of a rectangle whose sides are 24 cm and 7 cm is
(a) 25 cm
(b) 20 cm
(c) 26 cm
(d) 35 cm Question 17.
Which of the following can never be the measure of exterior angle of a regular polygon?
(a) 30°
(b) 36°
(c) 45°
(d) 22° Question 18.
ABCD is a parallelogram. Find the value of p
(a) 30°
(b) 100°
(c) 60°
(d) 80° Question 19.
Find the value of q
(a) 30°
(b) 36°
(c) 45°
(d) 70° Question 20.
Find the value of r
(a) 30°
(b) 100°
(c) 60°
(d) 80°
Answer
13. a
14. a
15. c
16. a
17. d
18. a
19. d
20. d
Summary
This Understanding quadrilaterals class 8 worksheets with Answers is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feebback on the mail.
