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Answers
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°