**Quadrilaterals Class 9 Worksheet**

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**Quadrilaterals Class 9 Worksheet**

**1.** If one
angle of a parallelogram is 105°, find the other angles.

**2.** If the
angles of a quadrilateral are 4*x*, 3*x *+ 10°, 2*x *+ 10° and 4*x
*+ 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 Î”ABC, 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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