﻿ Class 8 NCERT Math Solution
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TOPICS
Exercise - 3.2

Question-1 :-  Find x in the following figures.

Solution :-
```(a) By linear pair angle,
125° + m = 180°
m = 180° - 125°
m = 55°
By linear pair angle,
125° + n = 180°
n = 180° - 125°
n = 55°
Exterior angle x = sum of opposite interior angles
x = 55° + 55°
x = 110°
```
```(b) Sum of angles of a pentagon = (n-2) x 180° = (5-2) x 180° = 3 x 180° = 540°
By using of linear pair angles,
a + 90° = 180°
a = 180° - 90°
a = 90°

b + 60° = 180°
b = 180° - 60°
b = 120°

c + 90° = 180°
c = 180° - 90°
c = 90°

d + 70° = 180°
d = 180° - 70°
d = 110°

e + x = 180°
e = 180° - x

Now, a + b + c + d + e = 540°
90° + 120° + 90° + 110° + 180° - x = 540°
590° - x = 540°
x = 590° - 540°
x = 50°
```

Question-2 :-  Find the measure of each exterior angle of a regular polygon of
(i) 9 sides   (ii) 15 sides

Solution :-
```(i) Sum of angles of a regular polygon = (n-2) x 180° = (9 - 2) x 180° = 7 x 180° = 1260°
Each interior angle = sum of interior angles ÷ no. of sides = 1260° ÷ 9 = 140°
So, each exterior angle = 180° - 140° = 40°

(ii)Sum of exterior angles of a regular polygon = 360°
Each interior angle = sum of interior angles ÷ no. of sides = 360° ÷ 15 = 24°
```

Question-3 :-  How many sides does a regular polygon have if the measure of an exterior angle is 24°?

Solution :-
```  Let no. of sides be n.
Sum of exterior angles of a regular polygon = 360°
No. of sides = sum of exterior angles ÷ each inetrior angle = 360° ÷ 24° = 15
Hence, the regular polygon has 15 sides.
```

Question-4 :-  How many sides does a regular polygon have if each of its interior angles is 165°?

Solution :-
```  Let no. of sides be n.
Exterior angle = 180° - 165° = 25°
Sum of exterior angles of a regular polygon = 360°
No. of sides = sum of exterior angles ÷ each inetrior angle = 360° ÷ 15° = 24
Hence, the regular polygon has 24 sides.
```

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) No, because 22° is not divisior of 360°.
(b) No, because each exterior angle is 180° - 22° = 158°, which is not divisior of 360°.
```

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 Equilateral Trianglebeing a regular polygon of 3 sides has the last measure of an interior angles of 60°.
Sum of all angles of triangle = 180°
x + x + x = 180°
3x = 180°
x = 180°/3
x = 60°

(b) By first (a), we can observe that the greatest interior angle = 180° - 60° = 120°.
```
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