NCERT Solutions for Class 8 Maths Chapter 3- Understanding Quadrilaterals Exercise 3.3

The NCERT solutions for Class 8 maths Chapter 3- Understanding Quadrilaterals includes the solutions of all the questions present in the NCERT textbook. The subject experts at BYJU’S have solved each question of NCERT exercises with utmost care, in order to help the students in solving any question from the NCERT textbook. NCERT Class 8 Exercise 3.3 is based on the different types of quadrilaterals. Students can download the NCERT Solutions of Class 8 mathematics to furthermore understand the concept.

Download PDF of NCERT Solutions for class 8 Maths Chapter 3- Understanding Quadrilaterals Exercise 3.3

 

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Access other exercise solutions of Class 8 Maths Chapter 3- Understanding Quadrilaterals

Exercise 3.1 Solutions 7 Questions (1 Long Answer Questions, 6 Short Answer Questions)

Exercise 3.2 Solutions 6 Questions (6 Short Answer Questions)

Exercise 3.4 Solutions 6 Questions (1 Long Answer Questions, 5 Short Answer Questions)

Access Answers to Maths NCERT Class 8 Chapter 3- Understanding Quadrilaterals Exercise 3.3 Page Number 50

1. Given a parallelogram ABCD. Complete each statement along with the definition or property used.

NCERT Solution For Class 8 Maths Chapter 3 Image 14

(i) AD = …… (ii) ∠DCB = ……

(iii) OC = …… (iv) m ∠DAB + m ∠CDA = ……

Solution:

(i) AD = BC (Opposite sides of a parallelogram are equal)

(ii) ∠DCB = ∠DAB (Opposite angles of a parallelogram are equal) (iii) OC = OA (Diagonals of a parallelogram are equal)

(iv) m ∠DAB + m ∠CDA = 180°

2. Consider the following parallelograms. Find the values of the unknown x, y, z

NCERT Solution For Class 8 Maths Chapter 3 Image 15

Solution:

(i)

NCERT Solution For Class 8 Maths Chapter 3 Image 16

y = 100° (opposite angles of a parallelogram)

x + 100° = 180° (Adjacent angles of a parallelogram)

⇒ x = 180° – 100° = 80°

x = z = 80° (opposite angles of a parallelogram)

∴, x = 80°, y = 100° and z = 80°

NCERT Solution For Class 8 Maths Chapter 3 Image 17(ii)

50° + x = 180° ⇒ x = 180° – 50° = 130° (Adjacent angles of a parallelogram) x = y = 130° (opposite angles of a parallelogram)

x = z = 130° (corresponding angle)

(iii)

NCERT Solution For Class 8 Maths Chapter 3 Image 18

x = 90° (vertical opposite angles)

x + y + 30° = 180° (angle sum property of a triangle)

⇒ 90° + y + 30° = 180°

⇒ y = 180° – 120° = 60°

also, y = z = 60° (alternate angles)

(iv)

NCERT Solution For Class 8 Maths Chapter 3 Image 19

z = 80° (corresponding angle) z = y = 80° (alternate angles) x + y = 180° (adjacent angles)

⇒ x + 80° = 180° ⇒ x = 180° – 80° = 100°

(v)

NCERT Solution For Class 8 Maths Chapter 3 Image 20

x=28o

y = 112o z = 28o

3. Can a quadrilateral ABCD be a parallelogram if (i) ∠D + ∠B = 180°?

 

(ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?

(iii)∠A = 70° and ∠C = 65°?

Solution:

(i) Yes, a quadrilateral ABCD be a parallelogram if ∠D + ∠B = 180° but it should also

fulfilled some conditions which are:

(a) The sum of the adjacent angles should be 180°.

(b) Opposite angles must be equal.

(ii) No, opposite sides should be of same length. Here, AD ≠ BC

(iii) No, opposite angles should be of same measures. ∠A ≠ ∠C

4. Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.

 

Solution:

NCERT Solution For Class 8 Maths Chapter 3 Image 21

ABCD is a figure of quadrilateral that is not a parallelogram but has exactly two opposite

angles that is ∠B = ∠D of equal measure. It is not a parallelogram because ∠A ≠ ∠C.

5. The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of each of the angles of the parallelogram.

 

Solution:

Let the measures of two adjacent angles ∠A and ∠B be 3x and 2x respectively in

parallelogram ABCD.

∠A + ∠B = 180°

⇒ 3x + 2x = 180°

⇒ 5x = 180°

⇒ x = 36°

We know that opposite sides of a parallelogram are equal.

∠A = ∠C = 3x = 3 × 36° = 108°

∠B = ∠D = 2x = 2 × 36° = 72°

6. Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.

 

Solution:

Let ABCD be a parallelogram.

Sum of adjacent angles of a parallelogram = 180°

∠A + ∠B = 180°

⇒ 2∠A = 180°

⇒ ∠A = 90°

also, 90° + ∠B = 180°

⇒ ∠B = 180° – 90° = 90°

∠A = ∠C = 90°

∠B = ∠D = 90

°

7. The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.

 

NCERT Solution For Class 8 Maths Chapter 3 Image 22

Solution:

y = 40° (alternate interior angle)

∠P = 70° (alternate interior angle)

∠P = ∠H = 70° (opposite angles of a parallelogram)

z = ∠H – 40°= 70° – 40° = 30°

∠H + x = 180°

⇒ 70° + x = 180°

⇒ x = 180° – 70° = 110°

8. The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm)

 

NCERT Solution For Class 8 Maths Chapter 3 Image 23

Solution:

(i) SG = NU and SN = GU (opposite sides of a parallelogram are equal) 3x = 18

x = 18/3

⇒ x =6

3y – 1 = 26 an

d,

⇒ 3y = 26 + 1

⇒ y = 27/3=9

x = 6 and y = 9

(ii) 20 = y + 7 and 16 = x + y (diagonals of a parallelogram bisect each other) y + 7 = 20

⇒ y = 20 – 7 = 13 and,

x + y = 16

⇒ x + 13 = 16

⇒ x = 16 – 13 = 3

x = 3 and y = 13

9. In the above figure both RISK and CLUE are parallelograms. Find the value of x.

 

NCERT Solution For Class 8 Maths Chapter 3 Image 24

Solution:

∠K + ∠R = 180° (adjacent angles of a parallelogram are supplementary)

⇒ 120° + ∠R = 180°

⇒ ∠R = 180° – 120° = 60°

also, ∠R = ∠SIL (corresponding angles)

⇒ ∠SIL = 60°

also, ∠ECR = ∠L = 70° (corresponding angles) x + 60° + 70° = 180° (angle sum of a triangle)

⇒ x + 130° = 180°

⇒ x = 180° – 130° = 50°

10. Explain how this figure is a trapezium. Which of its two sides are parallel? (Fig 3.32)

 

NCERT Solution For Class 8 Maths Chapter 3 Image 25

Solution:

When a transversal line intersects two lines in such a way that the sum of the adjacent angles on the same side of transversal is 180° then the lines are parallel to each other. Here, ∠M + ∠L = 100° + 80° = 180°

Thus, MN || LK

As the quadrilateral KLMN has one pair of parallel line therefore it is a trapezium. MN and LK are parallel lines.

NCERT Solution For Class 8 Maths Chapter 3 Image 2611. Find m∠C in Fig 3.33 if AB || DC ?

 

Solution:

m∠C + m∠B = 180° (angles on the same side of transversal)

⇒ m∠C + 120° = 180°

⇒ m∠C = 180°- 120° = 60°

12. Find the measure of ∠P and ∠S if SP || RQ ? in Fig 3.34. (If you find m∠R, is there more than one

 

method to find m∠P?)

NCERT Solution For Class 8 Maths Chapter 3 Image 27

Solution:

∠P + ∠Q = 180° (angles on the same side of transversal)

⇒ ∠P + 130° = 180°

⇒ ∠P = 180° – 130° = 50°

also, ∠R + ∠S = 180° (angles on the same side of transversal)

⇒ 90° + ∠S = 180°

⇒ ∠S = 180° – 90° = 90°

Thus, ∠P = 50° and ∠S = 90°

Yes, there are more than one method to find m∠P.

PQRS is a quadrilateral. Sum of measures of all angles is 360°.

Since, we know the measurement of ∠Q, ∠R and ∠S.

∠Q = 130°, ∠R = 90° and ∠S = 90°

∠P + 130° + 90° + 90° = 360°

⇒ ∠P + 310° = 360°

⇒ ∠P = 360° – 310° = 50°


Exercise 3.3 of NCERT Solutions for Class 8 Maths Chapter 3- Understanding Quadrilaterals is based on the following topics:

  1. Kinds of Quadrilaterals
    1. Trapezium
    2. Kite
    3. Parallelogram
    4. Elements of a parallelogram
    5. Angles of parallelogram
    6. Diagonals of a parallelogram

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