In this page we have ** NCERT book Solutions for Class 8th Maths:quadilaterals** for
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**Question 1 **Find *x* in the following figures

a)

b)

**Answer - **We know that the sum of all exterior angles of any polygon is 360º.

(a) 125° + 125° + *x* = 360°

250° + *x* = 360°

*x* = 110°

b)

60° + 90° + 70° + *x* + 90° = 360°

310° + *x* = 360°

*x* = 50°

**Question 2**

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

(i) 9 sides

(ii) 15 sides

**Answer **

(i) Sum of all exterior angles of the given polygon = 360º

Each exterior angle of a regular polygon has the same measure.

Thus, measure of each exterior angle of a regular polygon of 9 sides

=360/9= **40 ^{0}**

ii) Sum of all exterior angles of the given polygon = 360º

Each exterior angle of a regular polygon has the same measure.

Thus, measure of each exterior angle of a regular polygon of 15 sides

=360/15=**24 ^{0}**

**Question 3**

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

**Answer**

Sum of all exterior angles of the given polygon = 360º

Measure of each exterior angle = 24º

Thus, number of sides of the regular polygon

=360/24=**15**

**Question 4**

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

**Answer - **Measure of each interior angle = 165°

Measure of each exterior angle = 180° − 165° = 15°

The sum of all exterior angles of any polygon is 360º.

Thus, number of sides of the polygon

=360/15=**24**

**Question 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?

**Answer **

The sum of all exterior angles of all polygons is 360º. Also, in a regular polygon, each exterior angle is of the same measure. Hence, if 360º is a perfect multiple of the given exterior angle, then the given polygon will be possible.

(a) Exterior angle = 22°

360º is not a perfect multiple of 22º. Hence, such polygon is not possible.

(b) Interior angle = 22°

Exterior angle = 180° − 22° = 158°

Such a polygon is not possible as 360° is not a perfect multiple of 158°.

**Question 6**

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

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

**Answer**

Consider a regular polygon having the lowest possible number of sides (i.e., an equilateral triangle). The exterior angle of this triangle will be the maximum exterior angle possible for any regular polygon.

**Exterior angle of an equilateral triangle** = 360/3=120

Hence, maximum possible measure of exterior angle for any polygon is 120º. Also, we know that an exterior angle and an interior angle are always in a linear pair.

Hence, **minimum interior angle** = 180º − 120° = 60º

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