Understanding Quadrilaterals - Solutions 2

CBSE Class –VIII Mathematics
NCERT Solutions
CHAPTER - 3
Understanding Quadrilaterals (Ex. 3.2)

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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 the 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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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$360/15$

                                   = 24 degrees

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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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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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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∘.${60}^{\circ }.$

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

= 180∘$180{}^{\circ }$

∴$\therefore$ 

 

 

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

.