Step-by-step explanation:

1.

i) Quadrilateral (Sum of exterior angles = 360)

II) Triangle ( Sum of interior angles = 180 < 360 )

iii) 9

iv) Decagon

v) 12 ( 360 / 30 )

vi)

vii) Square

viii) 360

ix) 10 ( 360 / 36 )

x) 8 ( Solving (n - 2)*180 = 135n )

2.

i) ii) & iv) are polygons

3.

i) (5 - 2)*180 = 3*180 = 540

ii) (7 - 2)*180 = 5*180 = 900

iii) (14 - 2)*180 = 12*180 = 2160

4.

i) (n - 2)*180 = 720

=> n - 2 = 4

=> n = 6

Six sides

ii) (n - 2)*180 = 1620

=> n - 2 = 9

=> n = 11

11 Sides

iii) 8 right angles = 8*90 = 720

(n - 2)*180 = 720

=> n - 2 = 4

=> n = 6

6 Sides

5.

All sides of octagon are EQUAL => regular octagon (8 sides)

=> 8 interior angles & All interior angles will also be equal

Sum of interior angles = (8 -2)*180 = 6*180 = 1080

Each interior angle = 1080/8 = 135°

6.

Sum of exterior angles of a polygon = 360

Measure of exterior angle of n sided regular polygon = 360/n

i) 360/6 = 60°

ii) 360/9 = 40°

iii) 360/15 = 24°

7.

Let the interior angles of a Pentagon be 2x, 3x, 4x, 5x & 6x

Sum of the interior angles = (5 - 2)*180 = 3*180 = 540

=> 2x + 3x + 4x + 5x + 6x = 540

=> 20x = 540

=> x = 27

2x = 54

3x = 81

4x = 108

5x = 135

6x = 162

Therefore the angles are 54°, 81°, 108°, 135° & 162°

8.

Let the polygon has n sides

=> polygon has n interior angles

of which 2 are right angles (90°) , remaining (n - 2) are 160°

Sum of interior angles of a polygon = (n - 2)*180

=> 90 + 90 + (n - 2)*160 = (n - 2)*180

=> 180 + (n - 2)*160 = (n - 2)*180

=> 180 = (n - 2)*20

=> n - 2 = 9

=> n = 11

Therefore, the polygon has 11 sides

9.

i) Equilateral Triangle

ii) Square

11.

Let the polygon has n angles & each exterior angle be 33°

Sum = 33n

Sum of exterior angles of a polygon = 360

=> 33n = 360

=> n = 10.90...

Since n is not a natural NUMBER, exterior angle cannot be 33°

12.

Let the polygon has n sides => n interior angles

Each interior angle is 162°

=> Sum = 162n

Sum of interior angles of a regular polygon = (n - 2)*180

=> 162n = (n - 2)*180

=> 162n = 180n - 360

=> 18n = 360

=> n = 20

Therefore, the polygon has 20 sides

13.

Let the polygon has n sides => n interior angles

Sum of n interior angles of a polygon = (n - 2)*180

Each interior angle = 115°

=> 115n = (n - 2)*180

=> 115n = 180n - 360

=> 65n = 360

=> n = 5.54

Since n is not a natural number, interior angle cannot be 115°

14.

Let the exterior & interior angles be 2x & 3x respectively

Sum of an interior angle & and an exterior angle = 180

=> 2x + 3x = 180

=> 5x = 180

=> x = 36

3x = 108

Each interior angle = 108°

Let the polygon has n sides => n interior angles

Sum = 108n

Sum of interior angles of a polygon = (n - 2)*180

=> 108n = (n - 2)*180

=> 108n = 180n - 360

=> 72n = 360

=> n = 5

Therefore, the polygon has 5 sides

15.

Sum of exterior angles of a polygon = 360°

Let the regular polygon has n sides

Each exterior angle = 360/n

This has to be maximum, which means n has to be minimum

minimum n = 3

=> exterior angle = 360/3 = 120°

Therefore, maximum exterior angle of a regular polygon = 120°