## Class 8 RS Aggarwal Maths Parallelograms Solutions - Free PDF Download

## FAQs on Quick and Easy RS Aggarwal Class 8 Mathematics Solutions for Chapter-16 Parallelograms

**1. The ratio between two adjacent angles of a ||gm ABCD are in the ratio 1 : 4. Find the angles.**

Let ∠ A = x and ∠ B = 4x

But ∠A + ∠B = 180°

=> x + 4x = 180°

=> 5x = 180°

∴ x = 180/5= 36°

∴ ∠A = Ax = 36°

∠B = 4x = 4 x 36 = 144° Ans.

**2. The sum of opposite angles of the parallelograms is 140°. Find the measure of all the angles. **

In ||gm ABCD, ∠A and ∠C are opposite angles.

∴ ∠A = ∠C= 140°

But ∠A = ∠C (opposite angles)

∴ ∠A = ∠C= 140°/2= 70°

But ∠A + ∠B = 180°

(sum of adjacent angles)

=> 70° + ∠B = 180°

=> ∠B = 180° – 70° = 110°

But ∠ D = ∠ B (opposite angles)

∴ ∠D = 110°

Hence ∠A = 70°, ∠B = 110°, ∠C = 70° and ∠ D = 110° Ans.

**3. ABCD is a parallelogram.AE and CF are the bisectors of ∠A and ∠C respectively. Prove that AE || CF.**

In ∆ADE and ∆CBF,

AD = BC

(Opposite sides of the parallelogram)

∠D = ∠B

(Opposite angles of the parallelogram)

∠DAE = ∠FCB (1/2 of equal angles)

∴ ∆ADE ≅ ∆CBF

(S.A.A. congruence)

∴ DE = BF (c.p.c.t.)

But CD = AB

(Opposite sides of the parallelogram)

∴ CD – DE = AB – BF

=> EC = AF

and AB || CD

∴ AFCE is a parallelogram

∴ AE || CF.

**4. List some properties of a parallelogram and name one of its special types.**

The properties of a parallelogram are-

A parallelogram is a special type of quadrilateral, in which its opposite sides are parallel and equal

The opposite angles of the parallelogram are also equal.

Adjacent angles in it are supplementary in nature, which means that the sum of two adjacent angles is equal to 180 degrees.

The two Diagonals of a parallelogram bisects each other at their mid-points

If any of the interior angles is 90 degrees, then all of them will be right angles.

Parallelograms are of various types, one such special type of it is Rhombus.

**5. How many exercises are there in the Chapter 16 parallelogram of class 8?**

If you follow Vedantu’s solution for Chapter 16 Parallelogram of class 8 has only two exercises 16 A and 16 B. Exercise 16 A contains 14 and 16 B contains 10 questions. Solutions to all of which are available in the RS Aggarwal class 8 maths solutions for chapter 16 provided by the Vedantu. In 16 A, students will encounter questions regarding the properties of parallelograms. And in exercise 16 b, questions will be based on the properties of diagonals of square, rhombus, and parallelograms.