NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2
These NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Questions and Answers are prepared by our highly skilled subject experts.
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise 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°
⇒ 250° + x = 360°
⇒ x = 360° – 250°
⇒ x = 110°
(b) x + 90° + 60° + 90° + 70° = 360°
⇒ x + 310° = 360°
⇒ x = 360° – 310°
⇒ x = 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
The given polygon is a regular polygon
All the exterior angles are equal
Measure of an exterior angle = 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 = 360∘/15 = 24°
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 sides = 360∘/24∘ = 15
Thus, there are 15 sides of the regular polygon.
Question 4.
How many sides does a regular polygon have if each of its interior angles is 165°?
Solution:
The given polygon is a regular polygon.
Each interior angle = 165°
Each exterior angle =180° – 165° = 15°
Number of sides = 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 = 360∘/22∘=180∘/11∘
If it is a regular polygon, then its number of sides must be a whole number.
Here 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°) = 158° is an exterior angle.
∴ Number of sides = 360∘/158∘=180∘/79∘
180∘/79∘ is not a whole number
∴ 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 is 60°.
(b) The sum of an exterior angle and its corresponding interior angle is 180°.
Minimum interior angle of a regular polygon is 60°.
∴ The maximum exterior angle of a regular polygon = 180° – 60° = 120°
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