## RS Aggarwal Class 8 Solutions Chapter 16 Parallelograms Ex 16B

These Solutions are part of RS Aggarwal Solutions Class 8. RS Aggarwal Solutions Class 8 Chapter 16 Parallelograms Ex 16B.

**Other Exercises**

- RS Aggarwal Solutions Class 8 Chapter 16 Parallelograms Ex 16A
- RS Aggarwal Solutions Class 8 Chapter 16 Parallelograms Ex 16B

**Questions Tick the correct answer in each of the following.**

**Question 1.**

**Solution:**

Answer = (c)

The diagonals of a rhombus are not necessarily equal but the diagonals in rectangle, square and isosceles trapezium are always equal.

**Question 2.**

**Solution:**

Answer = (c)

Each side of a rhombus

**Question 3.**

**Solution:**

Answer = (b)

The sum of adjacent angles of a || gm = 180°

2x + 25° + 3x – 5° = 180°

=> 5x + 20° = 180°

=> 5x = 180° – 20° = 160°

=> x = \(\\ \frac { 160 }{ 5 } \)

= 32°

**Question 4.**

**Solution:**

Answer = (a)

The diagonals in rhombus, kite intersect each other at right angles.

But the diagonals of parallelogram do not necessarily intersect at right angles.

**Question 5.**

**Solution:**

Answer = (c)

Let l = 4x, b = 3x,

Then (diagonal)² = l² + b²

=> (25)² = 16x² + 9x²

=> 25x² = 625

=> x² = 25

=> x = 5

=> l = 4x = 4 x 5 = 20cm

b = 3x = 3 x 5 = 15cm

Perimeter = 2(l + b) = 2 (20 + 15)

= 2 x 35 = 70 cm

**Question 6.**

**Solution:**

Answer = (d)

AP and BP are the bisector of ∠A and ∠B

Sum of two adjacent angles of a ||gm = 180°

or ∠A + ∠B = 180°

But ∠1 = \(\\ \frac { 1 }{ 2 } \) ∠A and ∠2 =\(\\ \frac { 1 }{ 2 } \) ∠B

∠1 + ∠2 = \(\\ \frac { 1 }{ 2 } \) ∠A + \(\\ \frac { 1 }{ 2 } \) ∠B

= \(\\ \frac { 1 }{ 2 } \) (∠A + ∠B)

= 180° x \(\\ \frac { 1 }{ 2 } \) = 90°

∠P = 180° – (∠1 + ∠2)

= 180° – 90° = 90°

**Question 7.**

**Solution:**

Answer = (b)

Let one adjacent angle = x

Then second angle (smallest) = \(\frac { 2 }{ 3 } x \)

x + \(\frac { 2 }{ 3 } x \) = 180°

= \(\frac { 5 }{ 3 } x \) = 180°

=> x = 180° x \(\\ \frac { 3 }{ 5 }\) = 108°

=> Smallest angle = 108° x \(\\ \frac { 2 }{ 3 }\) = 72°

**Question 8.**

**Solution:**

Answer = (a)

The diagonals of square, rhombus bisect the interior angle but the diagonals of a rectangle do not.

**Question 9.**

**Solution:**

Answer = (d)

Sides of a square are equal

2x + 3 = 3x – 5

=> 3x – 2x = 3 + 5

=> x = 8

**Question 10.**

**Solution:**

Answer = (c)

Let smallest angle = x

then largest angle = 2x – 24°

But x + 2x – 24° = 180°

=> 3x – 24° = 180°

=> 3x = 180° + 24 = 204°

=> x = \(\\ \frac { 204 }{ 3 }\) = 68°

largest angle = 180° – 68° = 112°

Hope given RS Aggarwal Solutions Class 8 Chapter 16 Parallelograms Ex 16B are helpful to complete your math homework.

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