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### Maths Assignment Class VIII | Quadrilateral Ch-11

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# Math Assignment Class VIII

# Understanding Quadrilateral

# Understanding Quadrilateral

# chapter - 11, class - 8

**Question 1**

**(i) Two adjacent angles of a parallelogram are (5x + 65) ^{o}
and (85 – 2x)^{o}. Find the measure of each angle of a parallelogram.**

**(ii) Two adjacent angles of a parallelogram are of measure (4x + 2) ^{o} and (3x - 4)^{o}. Find the measure of each angle of the parallelogram.**

**(iii) Two adjacent angles of a parallelogram are in the ratio 1 : 2. Find all the angles of parallelogram.**

**Question 2**

**A pair of adjacent sides of a rectangle is in the ratio of 5 : 12. If the length of the diagonal is 26 cm. Find the lengths of sides and perimeter of the rectangle.**

**Question 3**

**ABCD is a rectangle in which DP and BQ are perpendiculars from D and B respectively on diagonal AC. Show that :**

**(i) △ADP ≅ ****△****CBQ**

**(ii) ∠ADP = ∠CBQ**

**(iii) DP = BQ**

**Question 4**

**In the given figure ABCD is a parallelogram. If ∠DAB=
75 ^{o} and ∠DBC= 60^{o}, Calculate ∠CDB and ∠ADB**

**Question 5**

**Question 6Two adjacent angles of a rhombus are in the ratio 2 : 3. Find all the
angles of the rhombus. **

**Question 7**

**In the given figure both RIsK and ClUE are parallelogram. Find the value of x.**

**Question 8**

**PQRS is a rhombus. If ∠PSQ = 55**

^{o}, find all the angles of the rhombus.**Question 9**

**In the given parallelogram PQRS, O is the mid point of SQ. Find ∠S, ∠R, PQ, QR and diagonal PR.**

**Question 10**

**In the figure, l || m and 't' is the transversal. The angle bisectors of interior angles intersect at P and Q. Find the values of angles x and y.**

**Question 11**

**Find the measure of ∠x in the given figure.**

**Question 12**

**The lengths of a pair of adjacent sides of a rectangle are in the ratio 3 : 4. If its diagonal is 50 cm, find the lengths of the sides and hence, the perimeter of the rectangle.**

**Question 13**

**Exterior angle of a parallelogram is 100**

^{o}. Find the angles of parallelogram ?

**Question 15**

**The diagonals of a rectangle ABCD intersect at O. If ∠BOC = 68**

^{o}, find ∠ODA.

**Question 16**

**ABCD is a rhombus and its
diagonals intersect at O.**

**(i) Is △BOC ≌ △DOC ? State the congruence condition used.**

**(ii) Also state, if ∠BCO = ∠DCO**

**Question 17**

**In the given figure the exterior angle ABX of parallelogram
ABCD is 70 ^{o} and O is the mid point of diagonal BD, Find ∠BAD and ∠ADC.
Also find the length of diagonal AB, when OC = 3 cm.**

**Question 18**

**In given figure, ABCD is a rectangle and diagonals intersect
at O. If ∠AOB = 108 ^{o}, find**

**(i) ∠ABO (ii) ∠ADO (iii) ∠OCB**

**Question 19**

**In the given figure, PQRS is a rectangle, If ∠PRQ = 30**

^{o}, find the value of ∠PQS.**Question 20**

**The lengths of the diagonals of a rhombus are in ratio 6 : 8. If its perimeter is 40 cm. Find the length of the shorter diagonal.**

**Question 21**

**Find the measure of x in the given figure**

**Question 23.**

**A diagonal and a side of a rhombus are of equal length. Find the measure of the angles of the rhombus.**

**THANKS FOR YOUR VISIT**

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