Understanding Quadrilaterals - Solutions 2
CBSE Class –VIII Mathematics
NCERT Solutions
CHAPTER - 3
Understanding Quadrilaterals (Ex. 3.2)
NCERT Solutions
CHAPTER - 3
Understanding Quadrilaterals (Ex. 3.2)
1. Find
in the following figures:


Ans. (a) Here,

[Linear pair]



And

[Linear pair]


Exterior angle
= Sum of opposite interior angles


(b) Sum of the angles of a pentagon
= 

= 

= 


By linear pairs of angles,





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







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 exterior angle =
= 24 degrees
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.
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.
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
)

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
Sum of all the angles of a triangle
=





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

