Gujarat Board GSEB Textbook Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Textbook Questions and Answers.
Gujarat Board Textbook Solutions Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2
Question 1.
Find x in the following figures.
Solution:
(a) Sum of all the exterior angles of a polygon = 360°
∴ 125° + 125° + x = 360°
or 250° + x = 360°
or x = 360° – 250° = 110°
(b) ∵ x + 90° + 60° + 90° + 70° = 360°
or x + 310° = 360°
or x = 360° – 310° = 50°
Question 2.
Find the measure of each exterior angle of a regular polygon of
(i) 9 sides
(ii) 15 sides
Solution:
(i) Number of sides (n) = 9
Number of exterior angles = 9
Since, sum of all the exterior angles = 360°
∴ The given polygon is a regular polygon.
∵ All the exterior angles are equal.
∴ Measure of an exterior angle = \(\frac { 360° }{ 9 }\) = 40°
(ii) Number of sides of regular polygon =15
∴ Number of equal exterior angles =15
The sum of all the exterior angles = 360°
∴ The measure of each exterior angle
= \(\frac { 360° }{ 15 }\)
Question 3.
How many sides does a regular polygon have if the measure of an exterior angle is 24°?
Solution:
For a regular polygon, measure of each angle is equal.
∴ Sum of all the exterior angles = 360°
Measure of an exterior angle = 24°
∴ Number of angles = \(\frac { 360° }{ 24° }\) =15
Thus, there are 15 sides of the polygon.
Question 4.
How many sides does a regular polygon have if each of its interior angles is 165°?
Solution:
The given polygon is regular polygon.
Each interior angle = 165°
Each exterior angle = 180° – 165° =15°
Number of sides = \(\frac { 360° }{ 15° }\) = 24
Thus, there are 24 sides of the polygon.
Question 5.
(a) Is it possible to have a regular polygon with measure of each exterior angle 22°?
(b) Can it be an interior angle of a regular polygon? Why?
Solution:
(a) Each exterior angle = 22°
Number of sides = \(\frac { 360° }{ 22° }\) = \(\frac { 180 }{ 11 }\)
If it is a regular polygon, then its number of sides must be a whole number.
Here, \(\frac { 180 }{ 11 }\) is not a whole number.
∴ 22° cannot be an exterior angle of a regular polygon.
(b) If 22° is an interior angle, then 180° -22°, i.e., 158° is an exterior angle.
∴ Number of sides = \(\frac { 360° }{ 158° }\) = \(\frac { 180° }{ 79 }\)
which is not a whole number.
Thus, 22° cannot be an interior angle of a regular polygon.
Question 6.
(a) What is the minimum interior angle possible for a regular polygon? Why?
(b) What is the maximum exterior angle possible for a regular polygon?
Solution:
(a) The minimum number of sides of a polygon 3
The regular polygon of 3-sides is an equilateral triangle.
∴ Each interior angle of an equilateral triangle = 60°
Hence, the minimum possible interior angle of a polygon = 60°
(b) ∵ The sum of an exterior angle and its corresponding interior angle is 180°
And minimum interior angle of a regular polygon = 60°
The maximum exterior angle of a regular polygon – 180° – 60° = 120°