Understanding Quadrilaterals Exercise 3.2

NCERT solutions for Class 8 Maths Understanding Quadrilaterals 

NCERT Solutions for Class 8 Maths Understanding Quadrilaterals

Class –VIII Mathematics (Ex. 3.2)

NCERT SOLUTION

1. Find  in the following figures:

Ans. (a) Here,

[Linear pair]

 

And 

[Linear pair]

 

$\because$ Exterior angle

= Sum of opposite interior angles

$\therefore$ 

(b) Sum of angles of a pentagon

=

=

=

By linear pairs of angles,

  ……….(i)

  ……….(ii)

  ……….(iii)

  ……….(iv)

   ……….(v)

Adding eq. (i), (ii), (iii), (iv) and (v),

 

 

 

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NCERT Solutions for Class 8 Maths Exercise 3.2

2. Find the measure of each exterior angle of a regular polygon of:

(a) 9 sides

(b) 15 sides

Ans. (i) Sum of angles of a regular polygon =

=

Each interior angle =

Each exterior angle =

(ii) Sum of exterior angles of a regular polygon =

Each interior angle =

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3. How many sides does a regular polygon have, if the measure of an exterior angle is

Ans. Let number of sides be

Sum of exterior angles of a regular polygon =

Number of sides =

Hence, the regular polygon has 15 sides.

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NCERT Solutions for Class 8 Maths Exercise 3.2

4. How many sides does a regular polygon have if each of its interior angles is

Ans. Let number of sides be

Exterior angle =

Sum of exterior angles of a regular polygon =

Number of sides =

Hence, the regular polygon has 24 sides.

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5. (a) Is it possible to have a regular polygon with of each exterior angle as

(b) Can it be an interior angle of a regular polygon? Why?

Ans. (a) No. (Since 22 is not a divisor of )

(b) No, (Because each exterior angle is  which is not a divisor of )

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NCERT Solutions for Class 8 Maths Exercise 3.2

6. (a) What is the minimum interior angle possible for a regular polygon? Why?

(b) What is the maximum exterior angle possible for a regular polygon?

Ans. (a) The equilateral triangle being a regular polygon of 3 sides has the least measure of an

interior angle of ${{60}^{\circ }}.$

$\because$ Sum of all the angles of a triangle

= $180{}^\circ$

$\therefore$ 

 

 

(b) By (a), we can observe that the greatest exterior angle is

.

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