Thursday, 28 September 2023

POLYGON (A to Z)

1) Write in degrees the sum of all interior angles of a:
a) hexagon.                                       720
b) Septagon.                                     900
c) Nonagon.                                     1260
d) 15-gon.                                         2340

2) Find the measure, in degrees, of each interior angle of a regular.
a) pentagon.                                       108
b) octagon.                                         135
c) decagon.                                        144
d) 16-gon.                                         157.5

3) Find the measure, in degrees, of each exterior angle of a regular polygon containing :
a) 6 sides.                                             60
b) 8 sides.                                             45
c) 15 sides.                                           24
d) 20 sides.                                           18

4) Find the number of sides of a polygon, the sum of whose interior angles is:
a) 24 right angles.                              14
b) 1620.                                               11      
c) 2880.                                               18

5) Find the number of sides in a regular polygon, if each of its exterior angle is:
i) 72°.    5
ii)  24°.           15
iii) 22.5°.           16
iv) 15°.             24

6) Find the number of sides in a regular polygon, if each of its interior angles is
i) 120°.         6
ii)  150°.             12
iii) 160°.           18
iv) 165°.           24

7) Is it possible to describe a polygon, the sum of whose interior angle is :
a) 320°.            No
b)  540°.                  Yes
c)  11 right angles.       No
d) 14 right angles.      Yes

8) Is it possible to regular polygon, each of whose exterior angle is:
a) 32°.           Yes
b) 18°.       No
c) 1/8 of a right angle.     Yes
d) 89°.        No

9) Is it possible to have a regular polygon, each of whose interior angle is;
a) 120°.       Yes
b) 105°.       No
c)  175°.       Yes
d) 130°.       No

) Find the number of sides of a regular polygon, if each of its interior angle is 140°.   9

) Is it possible to have a regular polygon each of whose interior angle is 100°.  No

) The angles of a quadrilateral are in the ratio 6:3:2:4. Find the angles.     144, 72, 48, 96

) The angles of a pentagon are in the ratio 3:4:5:2:4. Find the angles.      90, 120, 150, 60, 120

) One angle of a polygon is 140°. If the remaining angles are in the ratio 1 :2 :3 :4, find the size of the greatest angle.         160°

) The angles of a pentagon are are (3x + 5)° , (x + 16)°, (2x + 9)°, (3x - 8)° and (4x - 15)° respectively. Find the value of x and hence find the measure of all the angles of the pentagon.             41, 128,57,91,115,149

) The angles of a hexagon are 2x°, ( 2x + 25)°,  3(x - 15)°, (3x - 20)°, 2(x +5)° and 3(x- 5)° respectively. Find the value of x and hence find the measure of all the angle of the hexagon.       51, 102,127,108,133,112,138

) Three of the exterior angles of a hexagon are 40°, 52° and 85° respectively and each of the remaining exterior angles is x°, find the value of x.         61

) One angle of an octagon is 100° and the other angles are all equal. Find the measure of each of the equal angles.          140

) The interior angle of a regular polygon is double the exterior angle. Find the number of sides in the polygon.             6

) The exterior angle of a regular polygon is 1/3 of its interior angle. Find the number of sides of the polygon.        8

) The ratio of each interior angle to each exterior angle of a regular polygon is 7:2. Find the number of sides in the polygon.          9

) The sum of the interior angle of a polygon is 6 times the sum of its exterior angles. Find the number of sides in the polygon.        14

) The sum of all the interior angles of a polygon is 2160°. How many side does the polygon have ?          14

) Two angles of a convex polygon are right angles and each of the other is 120°. Find the number of the sides of the polygon.       5

) The difference between an exterior angle of a regular polygonal of n sides and an exterior angle of a regular polygon of (n+1) sides is 5°. Find the value of n.    8

) The ratio between the number of sides of two polygons is 3:4 and the ratio between the sum of their interior angles is 2:3. Find the number sides in each polygon.    6,8

) The number of sides of two regular polygons are in the ratio 4:5 and  their interior angles are in the ratio 15:16. Find the number of sides of the each polygon.     8,10

) The number of sides of two regular polygons are in the ratio 1:2 and their interior angles are in the ratio 3:4. Find the number of sides and each polygon.         5,10

) Each interior angle of a regular polygon is 140°. Find the interior angle of a regular polygon which has double the number of sides as the first polygon.     160°

) In a polygon, there are 5 right angles and the remaining angles are 195° each. Find the number of sides in the polygon.          11


) How many diagonals are there in;
a)  pentagon .              5
b) hexagon.           9
c) octagon.               20

) The alternate sides of any pentagon are produced to meet, so as to form a star-shaped figure, shown in the figure.
 Prove that the sum of the measure of the angles of the vertices of the star is 180°.       


) ABCDE is a regular pentagon. Calculate 
a) each angle of BDE .         36
b) the ratio angAEB/angBED.            1/2

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