NCERT Solution (Ex-3.2) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 PDF Download

Understanding Quadrilaterals

Exercise 3.2

Question 1: Find x in the following figures:

Answer 1:
(a) Here, 125^o+m=180^o   [Linear pair]

 m=180^o-125^o = 55^o
and 125^o+n =180^o           [Linear pair]
n =180^o-125^o = 55^o
Exterior angle x^o = Sum of opposite interior angles
x^o = 55^o+55^o =110^o

(b) Sum of angles of a pentagon = (n - 2)x180^o
= (5 - 2)x180^o
= 3x180^o = 540^o

By linear pairs of angles,

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

Question 2:
Find the measure of each exterior angle of a regular polygon of:
(a) 9 sides

(b) 15 sides 

Answer 2:
(i) Sum of angles of a regular polygon = (n-2)x180^o
= (9-2)x180^o = 7x180^o =1260^o

Each interior angle= Sum of interior angles / Number of sides =1260^o/9 =140^o

Each exterior angle = 180^o-140^o = 40^o

(ii) Sum of exterior angles of a regular polygon = 360^o
Each interior angle = Sum of interior angles/Number of sides = 360^o/15 =24^o

Question 3:
How many sides does a regular polygon have, if the measure of an exterior angle is 24^o?

Answer 3:
Let number of sides be n.

Hence, the regular polygon has 15 sides.

Question 4:
How many sides does a regular polygon have if each of its interior angles is 165?

Answer 4:
Let number of sides be n.
Exterior angle = 180^o-165^o=15^o
Sum of exterior angles of a regular polygon = 360^o

Hence, the regular polygon has 24 sides.

Question 5:
(a) Is it possible to have a regular polygon with of each exterior angle as 22^o?
(b) Can it be an interior angle of a regular polygon? Why?

Answer 5:
(a) No. (Since 22 is not a divisor of 360^o )
(b) No, (Because each exterior angle is 180^o - 22^o =158^o, which is not a divisor of 360^o )

Question 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?

Answer 6:
(a) The equilateral triangle being a regular polygon of 3 sides has the least measure of an interior angle of 60^o .

 Sum of all the angles of a triangle = 180^o

 x+x+x= 180

 3x=180⁰

 x=60^o

(b) By (a), we can observe that the greatest exterior angle is 180⁰ - 60⁰ =120⁰.