# Understanding Quadrilaterals

## Exercise 3.2

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

(a)

(b)

Solution:

(a)

125^{0} + 125^{0} + *x*^{0} = 360^{0}

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

250^{0} + *x*^{0} = 360^{0}

*x*^{0} = 360^{0 }_{– }250^{0}

*x*^{0} = 110^{0}

(b)

60^{0} + 90^{0} + 70^{0} + *x*^{0} + 90^{0} = 360^{0}

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

310^{0} + *x*^{0} = 360^{0}

*x*^{0} = 360^{0 }_{– }310^{0}

*x*^{0} = 50^{0}

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}

= 40^{0}

(ii) 15 sides

The measure of the external angle of a regular polygon

= ^{360}/_{no. of angles}

= ^{360}/_{15}

= 24^{0}

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 = 180^{0} – 165^{0}

= 15^{0}

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 22^{0} as it is not a divisor of 360.

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

Measure of exterior angle = 180^{0} – 22^{0}

= 158^{0}

158 is not a divisor of 360

Therefore it is not possible to have a regular polygon with measure of each interior angle as 22^{0}.

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 60^{0}.

Therefore, minimum interior angle possible for a regular polygon is 60^{0}.

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

The maximum exterior angle possible for a regular polygon is 120^{0}.

Click here for the solutions of Std 8 Maths

1). Rational Numbers

2). Linear Equations in One Variable

3). Understanding Quadrilaterals

4). Data Handling