Rs Aggarwal 2017 Solutions for Class 8 Math Chapter 16 Parallelograms are provided here with simple step-by-step explanations. These solutions for Parallelograms are extremely popular among Class 8 students for Math Parallelograms Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2017 Book of Class 8 Math Chapter 16 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2017 Solutions. All Rs Aggarwal 2017 Solutions for class Class 8 Math are prepared by experts and are 100% accurate.

#### Question 1:

ABCD is a parallelogram in which ∠A = 110°. Find the measure of each of the angles ∠B,C and ∠D.

#### Question 2:

Two adjacent angles of a parallelogram are equal. What is the measure of each of these angles?

#### Question 3:

Two adjacent angles of a parallelogram are in the ratio 4 : 5. Find the measure of each of its angles. #### Question 4:

Two adjacent angles of a parallelogram are (3x − 4)° and (3x + 16)°. Find the value of x and hence find the measure of each of its angles. #### Question 5:

The sum of two opposite angles of a parallelogram is 130°. Find the measure of each of its angles. #### Question 6:

Two sides of a parallelogram are in the ratio 5 : 3. If its perimeter is 64 cm, find the lengths of its sides.

#### Question 7:

The perimeter of a parallelogram is 140 cm. If one of the sides is longer than the other by 10 cm, find the length of each of its sides.

#### Question 8:

In the adjacent figure, ABCD is a rectangle. If BM and DN are perpendiculars from B and D on AC, prove that ∆BMC ≅ ∆DNA. Is it true that BM = DN? Refer to the figure given in the book.

#### Question 9:

In the adjacent figure, ABCD is a parallelogram and line segments AE and CF bisect the angles A and C respectively. Show that AE||CF. Refer to the figure of the book.

#### Question 10:

The lengths of the diagonals of a rhombus are 16 cm and 12 cm respectively. Find the length of each of its sides. #### Question 11:

In the given figure ABCD is a square. Find the measure of ∠CAD. Refer to the figure given in the book.

#### Question 12:

The sides of a rectangle are in the ratio 5 : 4 and its perimeter is 90 cm. Find its length and breadth.

#### Question 13:

Name each of the following parallelograms.
(i) The diagonals are equal and the adjacent sides are unequal.
(ii) The diagonals are equal and the adjacent sides are equal.
(iii) The diagonals are unequal and the adjacent sides are equal.
(iv) All the sides are equal and one angle is 60°.
(v) All the sides are equal and one angle is 90°.
(vi) All the angles are equal and the adjacent sides are unequal.

#### Question 14:

Which of the following statements are true and which are false?
(i) The diagonals of a parallelogram are equal.
(ii) The diagonals of a rectangle are perpendicular to each other.
(iii) The diagonals of a rhombus are equal.
(iv) Every rhombus is a kite.
(v) Every rectangle is a square.
(vi) Every square is a a parallelogram.
(vii) Every square is a rhombus.
(viii) Every rectangle is a parallelogram.
(ix) Every parallelogram is a rectangle.
(x) Every rhombus is a parallelogram.

#### Question 1:

Tick (✓) the correct answer
The two diagonals are not necessarily equal in a
(a) rectangle
(b) square
(c) rhombus
(d) isosceles trapezium

#### Question 2:

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The lengths of the diagonals of a rhombus are 16 cm and 12 cm. The length of each side of the rhombus is
(a) 8 cm
(b) 9 cm
(c) 10 cm
(d) 12 cm #### Question 3:

Tick (✓) the correct answer
Two adjacent angles of a parallelogram are (2x + 25)° and (3x − 5)°. The value of x is
(a) 28
(b) 32
(c) 36
(d) 42

#### Question 4:

Tick (✓) the correct answer:
The diagonals do not necessarily intersect at right angles in a
(a) parallelogram
(b) rectangle
(c) rhombus
(d) kite

#### Question 5:

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The length and breadth of a rectangle are in the ratio 4 : 3. If the diagonal measures 25 cm then the perimeter of the rectangle is
(a) 56 cm
(b) 60 cm
(c) 70 cm
(d) 80 cm

(c) 70 cm

∴ P
erimeter of the rectangle = 2(20+15) cm

#### Question 6:

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The bisectors of any two adjacent angles of a parallelogram intersect at
(a) 30°
(b) 45°
(c) 60°
(d) 90°

#### Question 7:

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If an angle of a parallelogram is two-thirds of its adjacent angle, the smallest angle of the parallelogram is
(a) 54°
(b) 72°
(c) 81°
(d) 108°

#### Question 8:

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The diagonals do not necessarily bisect the interior angles at the vertices in a
(a) rectangle
(b) square
(c) rhombus
(d) all of these

#### Question 9:

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In a square ABCD, AB = (2x + 3) cm and BC = (3x − 5) cm. Then, the value of x is
(a) 4
(b) 5
(c) 6
(d) 8

#### Question 10:

Tick (✓) the correct answer:
If one angle of a parallelogram is 24° less than twice the smallest angle then the largest angle of the parallelogram is
(a) 68°
(b) 102°
(c) 112°
(d) 176°