Ncert Solutions For Class 8 Maths Ex 3.3

Ncert Solutions For Class 8 Maths Chapter 3 Ex 3.3

1. Given a parallelogram  ABCD. Complete each statement along with the definition or property used.
(i) AD = ……           (ii) DCB = ……
(iii) OC = ……         (iv)  DAB +  CDA = ……

Answer

(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 unknowns x, y, z.

1516181917

Answer

(a)

15

y = 100 (opposite angles of a parallelogram)

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

⇒ x = 180100= 80

x = z = 80 (opposite angles of a parallelogram)
Thus, x = 80, y = 100and y = 100

(b)

16

50+ x = 180⇒ x = 18050 = 130 (Adjacent angles of a parallelogram)
x = y = 130 (opposite angles of a parallelogram)
x = z = 130 (corresponding angle)

(c)

18

x = 90 (vertical opposite angles)

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

90 + y + 30 = 180
⇒ y = 180120 = 60
also, y = z = 60                                                                                                                                                                                                             (alternate angles)

(d)

19

z = 80 (corresponding angle)

z = y = 80 (alternate angles)

x + y = 180 (adjacent angles)

⇒ x + 80 = 180 ⇒ x 18080 = 100

 

(e)

17

y = 112  [Opposite angles are equal in a parallelogram

40+y+x=180 40+112+x=180 152+x=180 x=180152=28

and z = x = 28          [Alternate angles]

 

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 = 70and C = 65?

 Answer

(i)Yes, a quadrilateral ABCD be a parallelogram if D + B = 180but it should also fulfilled some conditions which are:

  • The sum of the adjacent angles should be 180
  • 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. AC

 

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

20

Answer

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 AC

 

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.

 Answer

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.

 Answer

Let ABCD be a parallelogram.

Sum of adjacent angles of a parallelogram =  180

A + B = 180

⇒ 2A = 180

A = 90

also, 90+ B  = 180

B = 18090= 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.

Answer

21

y = 40 (alternate interior angle)

P = 70 (alternate interior angle)

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

z = H40 = 7040 = 30

H + x = 180

70 + x = 180

⇒ x = 18070 = 110

 

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

 22

Answer

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

3x = 18

⇒ x = 18/3 = 6

3y – 1 = 26 and,

⇒ 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 below figure both RISK and CLUE are parallelograms. Find the value of x.

23

Answer

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

⇒ 120 + R = 180

R = 180120 = 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 = 180130 = 50

 

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

 24

Answer

 

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.

 

11. Find mC in Fig 3.33 if  AB || DC ?

 25

Answer

 

mC  + mB  = 180

(angles on the same side of transversal)

⇒mC  + 60

= 180

 

⇒mC 180

60

= 120

 

 

12. Find the measure of p andS if  SP || RQ ? in Fig 3.34. (If you find mR , is there more than one method to find mp ?)

 26

Answer

 

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  =50and S  = 90

 

Yes, there are more than one method to find mp .

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  = 90and S  = 90

p  + 130+ 90+ 90= 360

p  +310= 360

p  =360 310 = 50

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