Quadrilaterals Class 9 Worksheet with Answers
1. If one
angle of a parallelogram is 105°, find the other angles.
2. If the
angles of a quadrilateral are 4x, 3x + 10°, 2x + 10° and 4x
+ 15°, then find all the angles.
3. If the
angles of a quadrilateral are in the ratio 5 : 4 : 3 : 6, then find the angles.
4. Three
angles of a quadrilateral are 45°, 60°, 100°. Find the fourth angle.
5. If two
angles of a quadrilateral are 66° and 70° and the measure of other two angles are
equal, then find the angles.
6. Two
angles of a quadrilateral are 75° and 45°. If the measures of other two angles
are in the ratio 5 : 7, then find the measure of each angle.
7. ABCD is a quadrilateral in which the bisectors of ∠B and ∠C meet at O. If ∠A = 100° and ∠D = 70°, find the measure of ∠BOC.
8. A
quadrilateral has three interior angles each equal to 75°. Find the measure of
the fourth interior angle.
9. The
perimeter of a parallelogram is 60 cm. If the ratio of two of its sides is 3 :
2, find the length of its sides.
10. Two
adjacent angles of a parallelogram are in the ratio 1 : 2. Find the angles.
11. If the
sum of one pair of opposite angles of a parallelogram is 200°, find the angles
of the parallelogram.
12. The perimeter of a parallelogram is 100 cm. If one side is
10 cm longer than the other, find the sides of the parallelogram.
13. In the given figure, PQRS is a rectangle. Find
the value of x, y and z.
14. Three angles of a quadrilateral are in the ratio 4 : 6 : 5. If the measure of fourth angle is 60°, find all the angles.
15. The perimeter of
a kite is 106 cm. If one of its sides is 23 cm, find the lengths of the other
three sides.
16. In the following figure, PQRS is a parallelogram. Find each angle of the parallelogram marked
with a letter.
17. Two
consecutive angles of a parallelogram are in the ratio 2 : 3. Find the smaller angle.
18. If ABCD is rectangle with ∠BAC
= 32°, find the measure of ∠DBC.
19. The
diagonal of a rectangle ABCD intersect at the point O. If ∠BOC = 50°,
then find ∠OAD.
20. E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram.
21. Show that the line segment joining the mid-points of the opposite sides of a quadrilateral bisect each other.
22. The parallel sides of a trapezium are 7 cm and 5 cm respectively. Find the line segment joining the mid-points of its non-parallel sides.
23. In ΔABC, D and E are the mid-points of AB and AC respectively and DE = 5.6 cm. Find the length of BC.
24. A diagonal
of a parallelogram bisect one of its angles. Show that it’s a rhombus.
25. If an angle of a parallelogram is two-third of its adjacent angle, find the smallest angle of the parallelogram.
26. In a parallelogram ABCD, bisectors of ∠A and ∠B intersect at a point P. Find ∠APB.
27. If the diagonals of a rhombus are 18 cm and 24 cm respectively,
then find its sides.
28. ABCD is a
trapezium in which AB||CD and AD = BC. Show that ∠A
= ∠B.
ANSWERS
1. 75°, 105°, 75°, 105°
2. 100°, 85°, 60°, 115°
3. 100°, 80°, 60°, 120°
4. 155°
5. 112°, 112°
6. 100°, 140°
7. 85° 8. 135°
9. 18 cm, 12 cm, 18 cm, 12 cm
10. 60°, 120°
11. 100°, 80°, 100°, 80°
12. 20 cm, 30 cm
13. x = 60°, y = -1, z = 60°
14. 80°, 120°, 100°
15. 30 cm, 23 cm, 30 cm
16. x = 110°, y = 40°, z = 30°, t = 40°
17. 72° 18. 58°
19. 65°
20. Do it yourself
21. Do it yourself
22. 6 cm 23. 11.2 cm
24. Do it yourself
25. 72° 26. 90°
27. 15 cm
28. Do it yourself
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