Understanding Quadrilaterals

Exercise 3.2

1). Find x in the following figures.

(a)    

(b)

Solution:

(a)

125⁰ + 125⁰ + x⁰ = 360⁰

the sum of the measures of the external angles of any polygon is 360°.

250⁰ + x⁰ = 360⁰

x⁰ = 360⁰ _– 250⁰

x⁰ = 110⁰

(b)

60⁰ + 90⁰ + 70⁰ + x⁰ + 90⁰ = 360⁰

the sum of the measures of the external angles of any polygon is 360°.

310⁰ + x⁰ = 360⁰

x⁰ = 360⁰ _– 310⁰

x⁰ = 50⁰

2). Find the measure of each exterior angle of a regular polygon of

(i) 9 sides                                         (ii) 15 sides

Solution:

(i) 9 sides

 The measure of the external angle of a regular polygon

= ³⁶⁰/_{no. of angles}

= ³⁶⁰/₉

= 40⁰

(ii) 15 sides

The measure of the external angle of a regular polygon

= ³⁶⁰/_{no. of angles}

= ³⁶⁰/₁₅

= 24⁰

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

The number of sides of a regular polygon

= ³⁶⁰/_{measure of exterior angle}

= ³⁶⁰/₂₄

= 15

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

Measure of exterior angle = 180⁰ – 165⁰

                                         = 15⁰

The number of sides of a regular polygon

= ³⁶⁰/_{measure of exterior angle}

= ³⁶⁰/₁₅

= 24

5). (a) Is it possible to have a regular polygon with measure of each exterior angle as 22°?

No, it is not possible to have a regular polygon with measure of each exterior angle as 22⁰ as it is not a divisor of 360.

 

(b) Can it be an interior angle of a regular polygon? Why?

Measure of exterior angle = 180⁰ – 22⁰

                                         = 158⁰

158 is not a divisor of 360

Therefore  it is not possible to have a regular polygon with measure of each interior angle as 22⁰.

6). (a) What is the minimum interior angle possible for a regular polygon? Why?

An equilateral triangle is a regular polygon with minimum number of sides. Each angle of it is 60⁰.

Therefore, minimum interior angle possible for a regular polygon is 60⁰.

(b) What is the maximum exterior angle possible for a regular polygon?

The maximum exterior angle possible for a regular polygon is 120⁰.

Click here for the solutions of Std 8 Maths

1). Rational Numbers

 Exercise 1.1

2). Linear Equations in One Variable

Exercise 2.1

Exercise 2.2

3). Understanding Quadrilaterals

Exercise 3.1

Exercise 3.2

Exercise 3.3

Exercise 3.4

4). Data Handling

Exercise 4.1

Exercise 4.2