Ncert Solutions For Class 8 Maths Ex 3.2

Ncert Solutions For Class 8 Maths Chapter 3 Ex 3.2

 QUESTIONS-:

1Find the value of ‘p’ from the following figures

12

Ans.-(a)

13

Here, 125° + a = 180° => 180° – 125° = 55° (Linear pair)

125° + b = 180° =>180° – 125° = 55° (Linear pair)

p = a + b (exterior angle of a triangle is equal to the sum of two opposite interior two angles)

=> p = 55° + 55° = 110°

 

 

(b)

14

Two interior angles are right angles = 90°

70° + a = 180° => a = 180° – 70° = 110°    (Linear pair)

60° + b = 180° =>b = 180° – 60° = 120°    (Linear pair)
The given figure consisting of five sides and it is a pentagon.
Hence, the sum of the angles of a pentagon = 540°
90° + 90° + 110° + 120° + q = 540°
=>410° + y = 540° => q = 540° – 410° = 130°
p + q = 180°    (Linear pair)
=> p + 130° = 180°
=> p = 180° – 130° = 50°

 

2. Obtain the value for each of the exterior angle of a regular polygon with

(i) 10 sides           (ii) 25 sides

 

Ans.- Sum of angles a regular polygon having side a = (a-2)×180°
(i) Sum of angles a regular polygon having side 10 = (10-2)×180°
= 8×180° = 1440°
Each interior angle = 1440°/10 = 144°
Each exterior angle = 180° – 144° = 36°
Or,
Each exterior angle = Sum of exterior angles/Number of sides = 360°/10 = 36°

(i) Sum of angles a regular polygon having side 25 = (25-2)×180°
= 23×180° = 4140°
Each interior angle = 4140°/25 = 165.6°
Each exterior angle = 180° – 165.6° = 14.4°
Or,
Each exterior angle = Sum of exterior angles/Number of sides = 360°/25 = 14.4°

 

3. Calculate the number of sides a regular polygon will have if the value of an exterior angle is 36°?

Ans.-As we know that, Each exterior angle = Sum of exterior angles/Number of sides
So, 36° = 360°/Number of sides
=>Number of sides = 360°/36° = 10
Hence therefore, the regular polygon have 15 sides.

 

4. A regular polygon having each of its interior angles 144°. Calculate the number of sides it will have.

Ans.-Given, Interior angle = 144°
Exterior angle = 180° – 144° = 36°
Number of sides = Sum of exterior angles/exterior angle
=>Number of sides = 360°/36° = 10
Thus, the regular polygon have 10 sides.

 

5. (a) Can a regular polygon have each exterior angle with a measure of 37°?

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

 

Ans.-(a) Exterior angle = 22°
Number of sides = Sum of exterior angles/exterior angle
=>Number of sides = 360°/37° = 9.72
No, we cannot have a regular polygon with each exterior angle as 37° as it is not divisor of 360.

(b) Interior angle = 37°
Exterior angle = 180° – 37°= 143°
No, we can’t have a regular polygon with each exterior angle as 143° as it is not divisor of 360.

 

6. (a) Find the minimum possible interior angle for a regular polygon? Why?
(b) Find the maximum possible exterior angle for a regular polygon?

 

Ans.-(a)An equilateral triangle is a regular polygon having 3 sides with the least possible minimum interior angle as the regular polygon with minimum sides can be constructed with 3 sides at least..
Since, sum of the interior angles of a triangle = 180°
Each interior angle = 180°/3 = 60°

(b) Equilateral triangle is regular polygon with 3 sides has the maximum exterior angle because the regular polygon consisting least number of sides have the maximum exterior angle possible.
Maximum exterior possible = 180 – 60° = 120°