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

Class 8 CBSE Mathematics Guide and NCERT Solutions

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, 125O + 125O + x = 360O
x = 110O
(b)
60° + 90° + 70° + x + 90° = 360° ( 180O – 90O = 90O)
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 = 360O
Also, each exterior angle of a regular polygon has the same measure.
(i) Total number of sides = 9
Measure of each exterior angle = 360O ÷ 9 = 40O
(ii) Total number of sides = 15
Measure of each exterior angle = 360O ÷ 15 = 24O

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 = 360O
Given that each exterior angle of the regular polygon = 24O
∴ Number of sides = 360O ÷ 24O = 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 = 360O ÷ 15O = 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 = 360O ÷ (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 60O
(b) From the above we can see that the greatest Exterior Angle = 180º − 60º = 120º