Chapter 5: Understanding Quadrilaterals & Practical Geometry

Q21Written answer

If the adjacent sides of a parallelogram are equal then parallelogram is a

(a) rectangle (b) trapezium (c) rhombus (d) square

Show solutionHide solution

Worked solution

Solution:-

(c) rhombus

NCERT Exemplars Class 8 Maths Chapter 5 Image 10

Q22Written answer

If the diagonals of a quadrilateral are equal and bisect each other, then the quadrilateral is a

(a) rhombus (b) rectangle (c) square (d) parallelogram

Show solutionHide solution

Worked solution

Solution:-

(b) rectangle

Q23Written answer

The sum of all exterior angles of a triangle is

(a) 180^o (b) 360^o (c) 540^o (d) 720^o

Show solutionHide solution

Worked solution

Solution:-

(b) 360^o

The sum of all exterior angles of a triangle is 360^o

Q24Written answer

Which of the following is an equiangular and equilateral polygon?

(a) Square (b) Rectangle (c) Rhombus (d) Right triangle

Show solutionHide solution

Worked solution

Solution:-

(a) Square

Square is an equiangular and equilateral polygon.

Q25Written answer

Which one has all the properties of a kite and a parallelogram?

(a) Trapezium (b) Rhombus (c) Rectangle (d) Parallelogram

Show solutionHide solution

Worked solution

Solution:-

(b) Rhombus

Rhombus has all the properties of a kite and a parallelogram

Q26Written answer

The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. The smallest angle is

(a) 72^o (b) 144^o (c) 36^o (d) 18^o

Show solutionHide solution

Worked solution

Solution:-

(c) 36^o

We know that, sum of all interior angle of quadrilaterals is equal to 360^o.

Let us assume the angles be x, 2x, 3x, and 4x

Then,

x + 2x + 3x + 4x = 360^o

10x = 360^o

x = 360/10

x = 36

Therefore the angles are x = 36^o

2x = 2 × 36 = 72^o

3x = 3 × 36 = 108^o

4x = 4 × 36 = 144^o

Q27Written answer

In the trapezium ABCD, the measure of ∠D is

(a) 55^o (b) 115^o (c) 135^o (d) 125^o

NCERT Exemplars Class 8 Maths Chapter 5 Image 11

Show solutionHide solution

Worked solution

Solution:-

(d) 125^o

By observing the given figure ∠D and ∠A are supplementary.

We know that, sum of supplementary angle is equal to 180^o.

Then, ∠D + ∠A = 180^o

∠D + 55^o = 180^o

∠D = 180^o – 55^o

∠D = 125^o

Q28Written answer

A quadrilateral has three acute angles. If each measures 80°, then the measure of the fourth angle is

(a) 150^o (b) 120^o (c) 105^o (d) 140^o

Show solutionHide solution

Worked solution

Solution:-

(b) 120^o

We know that, sum of all interior angle of quadrilaterals is equal to 360^o.

Let us assume the fourth angle be x

Then,

80^o + 80^o + 80^o + x = 360^o

240^o + x = 360^o

x = 360^o – 240^o

x = 120^o

Q29Written answer

The number of sides of a regular polygon where each exterior angle has a measure of 45^o is

(a) 8 (b) 10 (c) 4 (d) 6

Show solutionHide solution

Worked solution

Solution:-

(a) 8

Now let us assume number of sides of a regular polygon be n.

WKT, sum of all exterior angles of all polygons is equal to 360^o.

Form the question it is given that each exterior angle has a measure of 45^o.

Then,

n × 45^o= 360^o

n = 360^o/45^o

n = 8

Q30Written answer

In a parallelogram PQRS, if ∠P = 60^o, then other three angles are

(a) 45^o, 135^o, 120^o (b) 60^o, 120^o, 120^o

(c) 60^o, 135^o, 135^o (d) 45^o, 135^o, 135^o

Show solutionHide solution

Worked solution

Solution:-

(b) 60^o, 120^o, 120^o

In parallelogram ∠P and ∠Q are supplementary.

We know that, sum of supplementary angle is equal to 180^o.

Then, ∠P + ∠Q = 180^o

∠60^o + ∠Q = 180^o

∠P = 180^o – 60^o

∠P = 120^o

And also, opposite angles ∠P and ∠R are equal in parallelogram.

So, ∠P = ∠R = 60^o

∠Q = ∠S = 120^o

Therefore, the other three angles of parallelograms are 60^o, 120^o and 120^o.

My Cart

Your Cart 0

Questions