Quadrilaterals

Exercise 3.2

Question 1: Find x in the following figures.

Class 8 math Quadrilaterals exercise 3.1-1

Solution: We know that sum of exterior angles of a polygon = 360⁰
So, `125° + 125° + x = 360°`
Or, `250° + x = 360°`
Or, `x = 360° = 250° = 110°`


Class 8 math Quadrilaterals exercise 3.1-2

Solution:

Class 8 math Quadrilaterals exercise 3.1-3

We know that sum of exterior angles of a polygon = 360⁰
So, `70° + x + 90° + 60° + 90° = 360°`
Or, `310° + x = 360°`
Or, `x = 360° - 310° = 50°`

Question 2: Find the measure of each exterior angle of a regular polygon of

(i) 9 sides

Solution: Since, 9 sides of a polygon has nine angles
And we know that sum of exterior angles of a polygon = 360⁰
So, 9 exterior angles = 360°
Or, 1 exterior angle `= 360°÷9 = 40°`

(ii) 15 sides

Solution: Since, 15 sides of a polygon has 15 angles
And we know that sum of exterior angles of a polygon = 360⁰
So, 15 exterior angles = 360°
Or, 1 exterior angle `= 360°÷15 = 24°`


Question 3: How many sides does a regular polygon have if the measure of an exterior angle is 24⁰?

Solution:We know that number of angles of a polygon = number of sides
And we know that sum of exterior angles of a polygon = 360⁰
So, measure of each angle = 24°
Or, number of exterior angles `= 360°÷24° = 15`
Hence, number of sides = 15

Question 4: How many sides does a regular polygon have if each of its interior angles is 165⁰?

Solution: Here, each interior angle = 165°
Hence, each exterior angle = 180° - 165° = 15°
As, measure of each exterior angle = 15°
So, number of sides `= 360°÷15° = 24`
Hence, number of sides = 24

Question 5: (a) Is it possible to have regular polygon with measure of each exterior angle as 22⁰?

Solution:
Since, number of sides of a polygon = 360°/each exterior angle
Hence, number of sides of given polygon `= 360°÷22° = 16.36`

Since, answer is not a whole number, thus, a regular polygon with measure of each exterior angle as 22⁰ is not possible.
Hence, Answer = no

(b) Can it be an interior angle of a regular polygon? Why?

Solution: Here, each interior angle = 22°
Hence, each exterior angle `= 180° - 22° = 158°`
Hence, number of sides `= 360°÷158° = 2.27`

Since, answer is not a whole number, thus, a regular polygon with measure of each interior angle as 22⁰ is not possible.
>Hence, Answer = no

Question 6: (a) What is the minimum interior angle possible for a regular polygon? Why?

Solution: Triangle is the polygon with minimum number of sides and an equilateral triangle is a regular polygon because all sides are equal in this. We know that each angle of an equilateral triangle measures 60 degree. Hence, 60 degree is the minimum possible value for internal angle of a regular polygon.

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

Solution: Each exterior angle of an equilateral triangle is 120 degree and hence this the maximum possible value of exterior angle of a regular polygon. This can also be proved by another principle; which states that each exterior angle of a regular polygon is equal to 360 divided by number of sides in the polygon. If 360 is divided by 3, we get 120.



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