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

**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 = = 40°

**ii) 15 sides**

**Solution:**

Total exterior angles = 15

Sum of exterior angles = 360°

Each exterior angle = = 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 = = 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 = = 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 = =

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 = =

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 =

Exterior angle is maximum when n is minimum

Minimum number of sides that a polygon can have is 3

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

Minimum interior angle

= 180° – Maximum exterior angle

= 180° – 120°

= 60°** Answer (a)**

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

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