NCERT Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise 3.2

The NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.2 emphasizes how to determine the sum of interior angles of various types of polygons, and, by using this property, to find unknown angles. The questions explore simple rules and logic that will make it easy to follow and solve.

The NCERT Solutions of Exercise 3.2 adheres to the latest NCERT Syllabus for Class 8 and is provided in a step by step manner with clear explanations. This helps develop a strong base for geometry problems in higher classes and competitive exams like Olympiads.

1.0Download NCERT Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise 3.2: Free PDF

Exercise 3.2 solves questions based on the angle sum property of quadrilaterals. The NCERT Solutions for Class 8 Maths Chapter 3 provides a structured way to learn and understand the material through step-by-step directions. Download the free PDF from below:

2.0Key Concepts in Exercise 3.2 of Class 8 Maths Chapter 3

This exercise explains how angles work inside polygons. Some of the important concepts in this exercise are:

• Angle sum property of quadrilaterals
• Formula to find sum of interior angles of polygons
• Finding unknown angles in given quadrilaterals
• Application of angle properties in problem-solving

3.0NCERT Class 8 Maths Chapter 3: Other Exercises

4.0NCERT Class 8 Maths Chapter 3 Exercise 3.2: Detailed Solutions

• Find x in the following figures : (a)
  
  (b)
  
  Sol. We know that the sum of the exterior angles formed by producing the sides of a convex polygon in the same order is equal to $360^{\circ }$. Therefore, (a) $x+125^{\circ }+125^{\circ }=360^{\circ }$ $\Rightarrow \mathrm{x}+250^{\circ }=360^{\circ }$ $\Rightarrow \mathrm{x}=360^{\circ }-250^{\circ }=110^{\circ }$ (b) $60^{\circ }+90^{\circ }+70^{\circ }+x+90^{\circ }=360^{\circ }$ $\Rightarrow 310^{\circ }+\mathrm{x}=360^{\circ }$ $\Rightarrow \mathrm{x}=360^{\circ }-310^{\circ }$ $\Rightarrow \mathrm{x}=50^{\circ }$
• Find the measure of each exterior angle of a regular polygon of (i) 9 sides (ii) 15 sides. Sol. (i) Each exterior angle of a regular polygon of 9 sides $=\frac{360^{\circ }}{\mathrm{n}}$, where $\mathrm{n}=9$ $\therefore {\left(\frac{360}{9}\right)}^{\circ }=40^{\circ }$ (ii) 15 sides Each exterior angle of a regular polygon of ' n ' sides $=$ where $\mathrm{n}=15$ $\therefore \frac{360^{\circ }}{15}=24^{\circ }$
• How many sides does a regular polygon have if the measure of an exterior angle is $24^{\circ }$ ? Sol. Since the number of sides of a regular polygon $=\frac{360^{\circ }}{\text{ Exterior angle }}$ Here, exterior angle $=24^{\circ }$ $\therefore$ Number of sides of the given polygon $=\frac{360^{\circ }}{24^{\circ }}=15$
• How many sides does a regular polygon have if each of its interior angles is $165^{\circ }$ ? Sol. Let there be n sides of the polygon. Then, its each interior angle $=$ $\therefore \frac{\mathrm{n}-2}{\mathrm{n}}\times 180^{\circ }=165^{\circ }$ $\Rightarrow 180^{\circ }\times \mathrm{n}-360^{\circ }=165^{\circ }\times \mathrm{n}$ $\Rightarrow 180^{\circ }\times \mathrm{n}-165^{\circ }\mathrm{n}=360^{\circ }$ $\Rightarrow 15^{\circ }\times \mathrm{n}=360^{\circ }$ $\Rightarrow \mathrm{n}=\frac{360^{\circ }}{15^{\circ }}=24$ Thus, there are 24 sides of the polygon.
• (a) Is it possible to have a regular polygon with measure of each exterior angle as $22^{\circ }$ ? (b) Can it be an interior angle of a regular polygon? Why? Sol. (a) Since the number of sides of a regular polygon $=\frac{360^{\circ }}{\text{ Exterior angle }}$ $\therefore$ The number of sides of a regular polygon $=\frac{360^{\circ }}{22}[\because$ Exterior angle $=22^{\circ }$, given $]$ $=\frac{180}{11}$ Which is not a whole number. $\therefore$ A regular polygon with measure of each exterior angle as $22^{\circ }$ is not possible. (b) If interior angle $=22^{\circ }$, then its exterior angle $=180^{\circ }-22^{\circ }=158^{\circ }$. But 158 does not divide $360^{\circ }$ exactly. Hence, the polygon is not possible.
• (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? Sol. (a) The equilateral triangle being a regular polygon of 3 sides has the least measure of an interior angle $=60^{\circ }$. (b) Since the minimum interior angle of a regular polygon is equal to $60^{\circ }$, therefore, the maximum exterior angle possible for a regular polygon $=180^{\circ }-60^{\circ }=120^{\circ }$.

5.0Key Features and Benefits of Class 8 Maths Chapter 3 Exercise 3.2

• They include questions on angle sum rules of polygons.
• The solutions follow the latest NCERT syllabus for Class 8 Maths.
• The solutions provide step-by-step explanations that make angles easier to learn.
• Practicing these solutions builds a good foundation in geometry for maths Olympiad preparation.
• Regularly solving these questions improves logical thinking and will make you more accurate in questions on angles.