 # NCERT Solutions for quadrilaterals Class 8 Maths Chapter 3 Exercise 3.2

In this page we have NCERT Solutions for quadrilaterals Class 8 Maths Chapter 3 for Exercise 3.2 . Hope you like them and do not forget to like , social share and comment at the end of the page.
Question 1
Find x in the following figures
a. b.

We know that the sum of all exterior angles of any polygon is 360º.
a. 125° + 125° +x= 360°
250° +x= 360°
x= 110°
b.
60° + 90° + 70° +x+ 90° = 360°
310° +x= 360°
x= 50°

Question 2
Find the measure of each exterior angle of a regular polygon of
(i) 9 sides
(ii) 15 sides
(i) Sum of all exterior angles of the given polygon = 360º
Each exterior angle of a regular polygon has the same measure.
Thus, measure of each exterior angle of a regular polygon of 9 sides
=360/9= 40°
(ii) Sum of all exterior angles of the given polygon = 360º
Each exterior angle of a regular polygon has the same measure.
Thus, measure of each exterior angle of a regular polygon of 15 sides
=360/15=24°

Question 3
How many sides does a regular polygon have if the measure of an exterior angle is 24°?
Sum of all exterior angles of the given polygon = 360º
Measure of each exterior angle = 24º
Thus, number of sides of the regular polygon
=360/24=15

Question 4
How many sides does a regular polygon have if each of its interior angles is 165°?
Answer -Measure of each interior angle = 165°
Measure of each exterior angle = 180° − 165° = 15°
The sum of all exterior angles of any polygon is 360º.
Thus, number of sides of the polygon
=360/15=24°

Question 5
(a) Is it possible to have a regular polygon with measure of each exterior angle as 22°?
(b) Can it be an interior angle of a regular polygon? Why?
The sum of all exterior angles of all polygons is 360º. Also, in a regular polygon, each exterior angle is of the same measure. Hence, if 360º is a perfect multiple of the given exterior angle, then the given polygon will be possible.
(a) Exterior angle = 22°
360º is not a perfect multiple of 22º. Hence, such polygon is not possible.
(b) Interior angle = 22°
Exterior angle = 180° − 22° = 158°
Such a polygon is not possible as 360° is not a perfect multiple of 158°.

Question 6
(a) What is the minimum interior angle possible for a regular polygon?
(b) What is the maximum exterior angel possible for a regular polygon?