# Maths Wiz Solutions Class 8 Chapter 10

## Maths Wiz Class 8 Solutions Chapter 10 Quadrilaterals

Welcome to NCTB Solutions. Here with this post we are going to help 8th class students for the Solutions of Maths Wiz Class 8 Math Book, Chapter 10, Quadrilaterals. Here students can easily find step by step solutions of all the problems for Quadrilaterals, Exercise 10A, 10B 10C, 10D and 10E Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 10 solutions. Here in this post all the solutions are based on ICSE latest Syllabus.

Question no – (1)

Solution :

Figure – (a)

The angle sum of a quadrilateral is 360°

125° + 105° + 75° + x° = 360°

= 305 + x° = 360°

= x° = 360° – 305°

= 55°

Figure – (b)

The angle sum of a quadrilateral is 360°

100° + 70° + 80° + y° = 360°

= 250° + y° = 360°

= y° = 360° – 250°

= 110°

Figure – (c)

The angle of sum of a quadrilateral is 360°

90° + 140° + a° + 30° = 360°

= 260° + a° = 360°

= a° = 360° – 260°

= 100°

Figure – (d)

The angle sum of a quadrilateral is 360°

20° + x° + 10° + 40° = 360°

= 70° + x° = 360°

= x° = 360° – 70°

= 290°

Figure – (e)

The angle sum of a quadrilateral is 360°

∴ P° + 70° + 90° + 90° = 360°

= P° + 250° = 360°

= P° = 360° – 250°

= 110°

Figure – (f)

The angle sum of a quadrilateral is 360°

138° + 90° + x° + 2x° = 360°

= 3x + 228° = 360°

= 3x = 360° – 228°

= x = 132/3

= x = 44

x° = 44

2x° = 2 × 44 = 88°

Figure – (g)

The angle sum of a quadrilateral is 360°

2m + m + m + 2m = 360°

= 6m = 360°

= m = 60°

2m = 2 × 60° = 120°

m = 60°

m = 60°

2m = 2 × 60° = 120°

Figure – (h)

The angle sum of a quadrilateral is 360°

65° + 240° + 30° + y° = 360°

= 335° + y° = 360°

= y° = 360° – 335°

= 25°

Question no – (2)

Solution :

Figure – (a)

= ∠C = 180° – 60° = 120°

∴ ∠A = 360° – {110°+ 120° + 50}

= 360° – 280°

= 80°

Figure – (b)

∠E = 180° – 35° = 145°

∠D = 180° – 145° = 35°

∠C = x° = 360° – {∠A + ∠B + ∠D}

= 360° – (90° + 136° + 35°)

= 360° – 261°

= 99°

Figure – (c)

3x + 4x + x + 2x = 360°

= 10x = 360°

= x = 36°

x = 36°

2 × x = 2 × 36° = 72°

3x = 3 × 36° = 108°

4x = 4 × 36° = 144°

Figure – (d)

∠D = 180° – 100° = 80°

∠C = 360° – {∠A + ∠b + ∠D}

= 360° – {90° + 70° + 80°}

= 360° – 240°

= 120°

Question no – (3)

Solution :

Let the measures of the angles be

2x, 4x, 6x, 8x

2x + 4x + 6x + 8x = 360°

= 20x = 360°

= x = 18°

measures of the angles be,

36°, 72°, 108°, 144°

Question no – (4)

Solution :

Sum of the angles of a quadrilateral 360°

x + 2x + 13° + 3x + 10° + x – 6° = 360°

= 7x° + 17° = 360°

= 7x = 360° – 17

= x = 343/7

= x = 49°

Therefore, the value of x will be 49°

Question no – (1)

Solution :

(a) A rectangle is a parallelogram.

= always

(b) A rhombus is a square.

= sometimes

(c) A parallelogram is a rhombus.

= sometimes

(d) A rhombus is a rectangle.

= sometimes

(e) A square is a rhombus.

= always

(f) A rectangle is a quadrilateral.

= always

(g) A square is a rectangle.

= always

(h) A rectangle is a square.

= sometimes

(i) A rectangle is a rhombus.

= Never

Question no – (2)

Solution :

A rhombus is equilateral but not equiangular. A rectangle is equiangular but not equilateral.

Question no – (1)

Solution :

Figure – (a)

x = 50° since opposite cones are equal

a = 8, b = 5 opposite sides are equal to

Figure – (b)

y = 3, x = 2

Figure – (c)

c = 95°

so, a + b = 360° – (95° + 95°)

= 360° – 190°

= 170°

so, a = 170/2 = 85

b = 170/2 = 85°

Figure – (d)

We knew x ≠ y

so, x + 2x + 2x + x = 360°

= 6x = 360°

= x = 60°

y = 60°

Figure – (f)

x = 6 opposite sides are equal

and 5y = 45°

= y = 15°

Question no – (2)

Solution :

∠AOD + ∠DOC = 230° = 360°

since AO = OD = OC

So, base cone are equal

∠AOC = ∠AOD + ∠DOC

∠AOC = 360 + 230

= 130°

a + A = 130°

= a = 65°

∠DAO + ∠AOD + ∠ADO = 180°

and ∠DOC + ∠DCO + ∠CDO = 180°

∠ADO = ∠DC = 180-65/2 = 575 each one is equal.

and opposite ∠ABC and ∠ADC are equal

= 2 × 57.5

= 115°

=  x = 115°

Therefore, the value of x will be 115°

Question no – (3)

Solution :

As we know, Same adjacent angle are 180°

∠A + ∠B = 180°

one the cones are 4x and 5x

So, 4x + 5x = 180°

x = 20°

∠A = 4 × 20 = 80°

∠B = 5 × 20 = 100°

similarly opposite cones

∠B + ∠C = 180°

= ∠C = 180 – 100

∠C = 80°

and ∠D = 180° – 80° = 100°

Therefore, the measures of the angles are ∠A = 80°, ∠B = 100°, ∠C = 80° and ∠D 100°

Question no – (4)

Solution :

5x – 21 + x + 75 = 180°

= 6x = 126

= x = 21

one cone ∠A = 5x – 21 = 105 – 21 = 84

∠B = x + 75 = 96

so, ∠C = 180° – 96° = 84°

and ∠D = 180° – 84 = 96°

Question no – (5)

Solution :

Side are 7x and 9x

We know perimeter

= (7x + 9x) = 96

= x = 96/2 × 16

= x = 3

side are = 7 × 3 = 21 cm

and = 9 × 3 = 27 cm

Therefore, the sides of the parallelogram are 21 cm and 27 cm.

Question no – (6)

Solution :

Figure – (a)

It is a Parallelogram

Figure – (b)

It is a Parallelogram

Reason : opposite sides are equal.

Figure – (c)

It is not a Parallelogram

Reason : opposite angles are equal.

Figure – (d)

It is not a parallelogram

Reason : the angle ∠ACB and ∠DAC are not equal.

Figure – (e)

It is not a parallelogram

Figure – (f)

It is not a parallelogram

Reason : opposite angles are not equal.

Question no – (7)

Solution :

Figure – (a)

8b = 10b – 3

= 10b – 8b = 3

= b = 1.5

Now, 5a – 15 = 3a – 5

= 5x – 3a = – 5 + 13

= 2a = 8

= a = 4

Figure – (b)

5b + 6 = 8a – 10

= 8a – 5b =16

= 8a + 16 = 5b

Again, 5b + 6 + 8a – 10 + 2 (4a – 8) = 360

= 5b + 6 + 8a – 10 + 8a – 16 = 360

= 8a + 16 + 6 + 8a – 10 + 8a – 16 = 360

= 24a = 360 + 16 + 10 – 16 – 6

a = 16.5, b = 23.2

Figure – (c)

5b – 7= 3b + 6

= 5b – 3b = 6 + 7

= 2b = 13

= b = 6.5

Now, 3b – 5 =2a

= 3 × 6.5 – 5 = 2a

= 19.5 – 5 = 2a

= 7.25 = a

Question no – (2)

Solution :

PQ = 20

Since, = SR = PQ

SK = 35/2 175 cm

Since, SK = SQ/2 = PR/2

Question no – (3)

Solution :

Figure – (a)

x = 7, y = 4

a = 90°,

b = 90°

c = 90°

d = 90°

Figure – (b)

∠x = 55°

∠y = (90° – 55) = 35°

Figure – (c)

15 = 5y

= y = 3

Now, 5x = 90°

x = 18°

Question no – (5)

Solution :

4a + 5 = 15a – 6

= 4a – 15a = – 6 – 5

= 11a = 11

= a = 1

So, sides are = 11 cm

So, BC = 11

Question no – (6)

Solution :

Figure – (a)

∠3 = 28°

∠2 = 28°

So, v5 = 28°

∠1 = 180 – (28 + 28)

= 124°

∠4 = 124°

Figure – (b)

∠4 = 50°

∠1 = 180 – 50/2

= 65

∠2 = 65°

∠3 = 65°

∠1 = 65°

∠5 = 65°

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Updated: June 19, 2023 — 2:02 pm