 # 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. Answer - 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?
Consider a regular polygon having the lowest possible number of sides (i.e., an equilateral triangle). The exterior angle of this triangle will be the maximum exterior angle possible for any regular polygon.
Exterior angle of an equilateral triangle  = 360/3=120
Hence, maximum possible measure of exterior angle for any polygon is 120º. Also, we know that an exterior angle and an interior angle are always in a linear pair.
Hence, minimum interior angle = 180º − 120° = 60º

Reference Books for class 8 Math

Given below are the links of some of the reference books for class 8 Math.

1. Mathematics Foundation Course for JEE/Olympiad : Class 8 This book can take students maths skills further. Only buy if child is interested in Olympiad/JEE foundation courses.
2. Mathematics for Class 8 by R S Aggarwal Detailed Mathematics book to clear basics and concepts. I would say it is a must have book for class 8 student.
3. Pearson Foundation Series (IIT -JEE / NEET) Physics, Chemistry, Maths & Biology for Class 8 (Main Books) | PCMB Combo : These set of books could help your child if he aims to get extra knowledge of science and maths. These would be helpful if child wants to prepare for competitive exams like JEE/NEET. Only buy if you can provide help to the child while studying.
4. Reasoning Olympiad Workbook - Class 8 :- Reasoning helps sharpen the mind of child. I would recommend students practicing reasoning even though they are not appearing for Olympiad.

You can use above books for extra knowledge and practicing different questions.

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