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 and comment at the end of the page.

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 180140 n=(n-2) \times 180n=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$2x + 2 \times 12 =38x=7$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.

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

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 $\angle YSR$

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.

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

So $2 \times 75 + 2x=360$x=105$Fill in the Blank Question 11. (i) Diagonals of a rectangle are __________. (ii)In an parallegram, adjacents angles are _____ (iii)The sum of all exterior angles of a polygon is __________. (iv)The measure of each exterior angle of a regular pentagon is __________. (v) The number of sides of a regular polygon whose each interior angle is of 135° is ___ Answer (i) equal (ii)equal (iii) 360° (iv) 72° (v) 8 True and False Question 12. (i) Diagonals of a rectangle are perpendicular to each other (ii)All angles of a trapezium are equal (iii)Every square is a trapezium. (iv)If diagonals of a quadrilateral are equal, it must be a rectangle. (v) Every square is a rhombus (vi) ALl parallelograms are kites but all kites are not parallelogram Answer (i) False (ii)False (iii) True (iv)false (v) false (vi) True Multiple Choice questions Question 13. The sum of angles of a concave quadrilateral is (a) more than 360° (b) less than 360° (c) equal to 360° (d) twice of 360° Question 14. The sum of adjacent angles of a parallelogram is (a) 180° (b) 120° (c) 360° (d) 90° Question 15. ABCD is a rectangle .F and E are the mid points of BC and CD respectively. If area of the$\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°

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.