NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.2 – Understanding Quadrilaterals, has been designed by the NCERT to test the knowledge of the student on the topic – Sum of the Measures of the Exterior Angles of a Polygon

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

**NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.2**

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

**a) **

**Solution:**

Sum of exterior angles = 360°

125° + 125° + x = 360°

250° + x = 360°

x = 360° – 250°

x = 110°

**b) **

**Solution:**

Sum of exterior angles = 360°

90° + 70° + x + 90° + 60° = 360°

310° + x = 360°

x = 360° – 310°

x = 50°

**Find the measure of each exterior angle of a regular polygon of**

**i) 9 sides**

**Solution:**

Total exterior angles = 9

Sum of exterior angles = 360°

Each exterior angle = (360°/9) = 40°

**ii) 15 sides**

**Solution:**

Total exterior angles = 15

Sum of exterior angles = 360°

Each exterior angle = (360°/15) = 24°

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

**Solution:**

Sum of exterior angles = 360°

Each exterior angle = 24°

Total number of exterior angles = (360°/24°) = 15

Therefore, the polygon has 15 sides.

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

**Solution:**

Each interior angle = 165°

Interior angle + exterior angle = 180°

165° + exterior angle = 180°

Exterior angle = 15°

Sum of exterior angles = 360°

Total number of exterior angles = (360°/15°) = 24

Therefore, the 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) Number of sides of a polygon with 22° as exterior angle = (360°/22°) = (180/11)

The number of sides cannot be a fraction

∴ A regular polygon cannot have each exterior angle as 22°

(b) Exterior angle = 180° – interior angle

Exterior angle = 180° – 22° = 158°

Number of sides of a polygon with 158° as exterior angle = (360°/158**°**) = (180/79)

The number of sides cannot be a fraction

∴ A regular polygon cannot have interior angle 22°

**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:**

Interior angle = 180° – Exterior angle

Interior angle is minimum for the polygon having maximum exterior angle

Let the polygon has n sides

Therefore, exterior angle = (360°/n)

Exterior angle is maximum when n is minimum

Minimum number of sides that a polygon can have is 3

Therefore maximum exterior angle = (360°/3) = 120° ** Answer (b)**

Minimum interior angle

= 180° – Maximum exterior angle

= 180° – 120°

= 60°** Answer (a)**

**The next Exercise for** **NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.3 – Understanding Quadrilaterals can be accessed by clicking here**

**Download NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.2 – Understanding Quadrilaterals**

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