Chapter 3 Understanding Quadrilaterals Exercise 3.2
Question 1.
Find x in the following figures.
![NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q1](https://rajboardexam.in/wp-content/uploads/2022/07/ncert-solutions-for-class-8-maths-chapter-3-unders.png)
Solution:
(a) We know that the sum of all the exterior angles of a polygon = 360°
125° + 125° + x = 360°
⇒ 250° + x = 360°
![NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q1.1](https://rajboardexam.in/wp-content/uploads/2022/07/ncert-solutions-for-class-8-maths-chapter-3-unders-1.png)
x = 360° – 250° = 110°
Hence x = 110°
(b) Here ∠y = 180° – 90° = 90°
![NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q1.2](https://rajboardexam.in/wp-content/uploads/2022/07/ncert-solutions-for-class-8-maths-chapter-3-unders-2.png)
and ∠z = 90° (given)
x + y + 60° + z + 70° = 360° [∵ Sum of all the exterior angles of a polygon = 360°]
⇒ x + 90° + 60° + 90° + 70° = 360°
⇒ x + 310° = 360°
⇒ x = 360° – 310° = 50°
Hence x = 50°
![](https://rajboardexam.in/wp-content/uploads/2022/07/word-image-66.png)
Question 3.
How many sides does a regular polygon have if the measure of an exterior angle is 24°?
Solution:
Sum of all exterior angles of a regular polygon = 360°
Number of sides
Hence, the number of sides = 15
Question 4.
How many sides does a regular polygon have if each of its interior angles is 165°?
Solution:
Let re be the number of sides of a regular polygon.
Sum of all interior angles = (n – 2) × 180°
and, measure of its each angle
Hence, the number of sides = 24
Question 5.
(a) Is it possible to have a regular polygon with measure of each exterior angle a is 22°?
(b) Can it be an interior angle of a regular polygon? Why?
Solution:
(a) Since, the sum of all the exterior angles of a regular polygon = 360° which is not divisible by 22°.
It is not possible that a regular polygon must have its exterior angle 22°.
(b) Sum of all interior angles of a regular polygon of side n = (n – 2) × 180°
not a whole number.
Since number of sides cannot be in fractions.
It is not possible for a regular polygon to have its interior angle = 22°.
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?
Solution:
(a) Sum of all interior angles of a regular polygon of side n = (n – 2) × 180°
The measure of each interior angle
The minimum measure the angle of an equilateral triangle (n = 3) = 60°.
(b) From part (a) we can conclude that the maximum exterior angle of a regular polygon = 180° – 60° = 120°.
![NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 A1](https://rajboardexam.in/wp-content/uploads/2022/07/ncert-solutions-for-class-8-maths-chapter-3-unders-7.png)
![NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 A1.1](https://rajboardexam.in/wp-content/uploads/2022/07/ncert-solutions-for-class-8-maths-chapter-3-unders-8.png)
![NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 A2](https://rajboardexam.in/wp-content/uploads/2022/07/ncert-solutions-for-class-8-maths-chapter-3-unders-9.png)
![NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 A3](https://rajboardexam.in/wp-content/uploads/2022/07/ncert-solutions-for-class-8-maths-chapter-3-unders-10.png)
![NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 A4](https://rajboardexam.in/wp-content/uploads/2022/07/ncert-solutions-for-class-8-maths-chapter-3-unders-11.png)
![NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 A5](https://rajboardexam.in/wp-content/uploads/2022/07/ncert-solutions-for-class-8-maths-chapter-3-unders-15.png)
![NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 A6](https://rajboardexam.in/wp-content/uploads/2022/07/ncert-solutions-for-class-8-maths-chapter-3-unders-16.png)