Understanding Quadrilaterals | CBSE Guide for Class 8 Mathematics | NCERT Solutions of Math Exercise 3.2

Class 8 CBSE Mathematics Guide and NCERT Solutions  

Chapter 3 Understanding Quadrilaterals

NCERT Solutions of Understanding Quadrilaterals Exercise 3.2

Question 1: Find x in the following figures.

Solution:

(a)

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

Therefore, 125^O + 125^O + x = 360^O

⇒ x = 110^O  

(b)

⇒ 60° + 90° + 70° + x + 90° = 360° (∴ 180^O – 90^O = 90^O)

⇒ 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

Solution: We know total measures of all exterior angles = 360^O

Also, each exterior angle of a regular polygon has the same measure.

(i) Total number of sides = 9

∴ Measure of each exterior angle = 360^O ÷ 9 = 40^O

(ii) Total number of sides = 15

∴ Measure of each exterior angle = 360^O ÷ 15 = 24^O

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

Solution: We know total measures of all exterior angles = 360^O

Given that each exterior angle of the regular polygon = 24^O

∴ Number of sides = 360^O ÷ 24^O = 15

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

Solution: Measure of each interior angle = 165°

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

⇒ Sum of all exterior angles of any polygon = 360º

∴ Number of sides = 360^O ÷ 15^O = 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?

Solution:

(a) The sum of all exterior angles of all polygons is 360º. In a regular polygon, each exterior angle is of the same measure. Hence, a regular polygon is possible only if 360º is a perfect multiple of the given exterior angle. In the given case the answer is ‘No’. (Since; 22° is not divisor of 360º).

(b) Given that interior angle = 22°

⇒ Exterior angle = 180° − 22° = 158°

In the given case the answer is ‘No’ because 158° is not divisor of 360º.

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?

Solution:

We know, measure of each exterior angle = 360^O ÷ (Number of sides of a regular polygon)

Hence, ‘Maximum Exterior Angle’ will be of a regular polygon with minimum sides and the same will have a minimum ‘Interior Angle’. Because,

Interior angle = 180º − Exterior Angle.

(a) The equilateral triangle being a regular polygon with only 3 sides has the least measure of Interior Angle 60^O

(b) From the above we can see that the greatest Exterior Angle = 180º − 60º = 120º  

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