Latest Updated : October 2023

If you are in search of **NCERT solutions for Class 8 Maths Chapter** **3 Understanding Quadrilaterals**, then you are at the right place. When it comes to **Mathematics**, it is a subject that holds value for students across various academic streams, be it science, biology, or commerce and having a very good understanding of basic math concepts will help you in achieving your goal and make it much more easier.

Here we provide detailed **NCERT solutions for Class 8 Maths** of all the chapters, **exercise wise** with **updated syllabus by NCERT**. These NCERT solutions for Class 8 Maths have been carefully crafted to provide detailed explanations, ensuring that students can grasp the concepts effectively. We also provide extra practice questions for the same, so feel free to bookmark **ncertforclass8.com** to boost your preparation.

## NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2

**Class 8 Maths Chapter** 3 Understanding Quadrilaterals **Exercise **3.2

**Exercise 3.2**

**1. Find x in the following figures.**

Solution:

(a) 125°+m=180° [Linear pair]

⇒m=180°-125°=55°

Also, 125°+n=180° [Linear pair]

⇒n=180°-125°=55°

Exterior angle x° = Sum of opposite interior angles

x°= 55° + 55°

x°= 110°

Solution:

(b) Sum of angles of a pentagon = (n-2)×180°

= (5-2)×180°

= 3×180°=540°

By linear pairs of angles,

∠1+90°=180° ………………………..(i)

∠2+60°=180° ……………………… (ii)

∠3+90°=180° ……………………… (iii)

∠4+70°=180° ………………………(iv)

∠5+x=180° ………………………..(v)

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

x+(∠1+∠2+∠3+∠4+∠5)+310°=900

⇒x+540°+310°=900°

⇒x+850°-900°

⇒x=900°-850°=50°

**2. Find the measure of each exterior angle of a regular polygon of(i) 9 sides (ii) 15 sides**

Solution:

(i) Sum of angles of a regular polygon = (n-2)×180°

= (9-2)×180°=7×180°=1260°

Each interior angle = Sum of interior angles/ Number of sides

= 1260°/9

= 140°

Each exterior angle= 180°-140° =40°

(ii) Sum of exterior angles of a regular polygon = 360°

Each interior angle = Sum of interior angles / Number of sides

= 360°/15

= 24°

**3.** **How many sides does a regular polygon have if the measure of an exterior angle is 24°?**

Solution:

Let the number of sides be x.

Sum of exterior angles of a regular polygon = 360°

Number of sides = Sum of exterior angles / Each interior angle

Number of sides = 360°/24°

Number of sides = 15

Hence, the regular polygon has 15 sides.

**4. How many sides does a regular polygon have if each of its interior angles is 165°?**

Solution:

Let the number of sides be n.

Exterior angle = 180° – 165° = 15°

Sum of exterior angles of a regular polygon = 360°

Number of sides = Sum of exterior angles / Each interior angle

= 360°/15 °

=24 sides

Hence, the regular polygon has 24 sides.

**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?**

Solution:

(a) No, its not possible to have a regular polygon with measure of each exterior angle as 22° since 22 is not a divisor of 360°

(b) No, it cannot be an interior angle of a regular polygon because each exterior angle is 180°-22°-158°, which is not a divisor of 360°

**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) The equilateral triangle being a regular polygon of 3 sides has the least measure of an interior angle of 60°

⇒Sum of all the angles of a triangle = 180°

⇒x+x+x=180°

⇒ 3x=180°

⇒x=60°

Therefore, the minimum interior angle possible for a regular polygon is 60°

(b) By (a), we can observe that the maximum exterior angle is 180°-60°=120°.

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**Accurate Answers:**NCERT solutions for Class 8 Maths are prepared by expert educators and thoroughly reviewed to ensure quality and accurate answers.**Aligned with Curriculum:**NCERT Solutions for Class 8 Maths are specifically designed to go along with the CBSE curriculum, making them the ideal resource for students studying in CBSE affiliated schools.**Crisp an Clear Explanation**: The NCERT solutions for Class 8 Maths provide step by step explanations, making complex concepts easier to understand. This helps students to grasp the concepts easily and build a better foundation.**Time-Saver:**Instead of spending extra time searching for answers, students can quickly access these NCERT solutions for Class 8 Maths , saving time and allowing them to focus on other aspects of their studies.**Extra Questions:**NCERT Solutions for Class 8 Maths also has extra questions that offer additional opportunities for students to build better problem solving skills.**Free Forever:**We provide answers which will always be free to access and share.**Self-Study Support:**These are beneficial for students who prefer self study. They can independently work through the solutions and improve their understanding of the subject at their own pace.

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