Understanding Quadrilaterals - Solutions 2

CBSE Class –VIII Mathematics
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,
   ……….(i)
   ……….(ii)
   ……….(iii)
   ……….(iv)
    ……….(v)
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 = 360/15
                                   = 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 60.
 Sum of all the angles of a triangle
180
 
 
 
(b) By (a), we can observe that the greatest exterior angle is 
.