F.2 Eng Math (急急急20點急急急)

As the sum of interior angle of regular triangle is 60 x 3 = 180
the sum of interior angle of regular square is 90 x 4 = 360

We can get below squence between the interior angle and number of sides:

180(x-2)/x , while x is not smaller than 3 and is a integer

Therfore, for interior angle 180

180(x-2)/x = 108
180x - 360 = 108x
x = 5

for interior angle 162

180(x-2)/x = 162
180x -360 = 162x
x = 20

Q1.
let x be the number of sides
x = 360 / (180 - 108)
x = 360 / 72
x = 5

Q2.
let y be the number of sides
y = 360 / (180 - 162)
y = 360 / 18
y = 20

Q1.
No. of side=1
Because an angle on straight is 180°
Q2.
Let X be the no. of sides of polygon
(X-2)180°/X=162°
180°X-360°=162°X
18°X=360°
X=20
∴The no. of sides of polygon is 20
(Note:No. =number)

2008-02-23 18:51:26 補充：
Q1Let Y be the no. of sides of polygon(Y-2)180°/Y=108°180°Y-360°=108°Y72°Y=360°Y=5∴The no. of sides of polygon is 5

1.
impossible
180∘is a straight line

2.
let n be the number of sides
(n-2)*180∘= n*162∘
180n - 360 = 162n
18n = 360
n = 20
∴ number of sides is 20

2008-02-23 21:35:12 補充：
THEN..1.let n be the number of sides(n-2)*180∘= n*108∘180n-360 = 108n72n = 360n = 5