有條數唔識做,求高人解答...急!!!!!!!!!

Ina regular polygon, each interior angle isthree times the exterior angle.
(a) Find the size of each exterior angle.
(b) Find the size of each interior angle.
(c) Name the regular polygon.


(a)
Let n be the number of sides of the regular polygon.

Since the sum of all exterior angles is 360°,
then each exterior angle = 360°/n
and each interior angle = 180° - (360°/n)

Eachinterior angle isthree times the exterior angle:
180 - (360/n) = 3(360/n)
180n - 360 = 1080
180n = 1440
n = 8

Each exterior angle = 360°/8 = 45°


(b)
Each interior angle = 3 * 45° = 135°


(c)
octagon

2011-08-15 16:31:12 補充：
樓上 Spider 所用的「嘗試」方法不可取。等同於解方程時（solving equation），不斷用數字代入（substitute into）方程中，以令兩邊兩等的數字為解（solution），這樣「嘗試」的方法在考試時是不接受的。

圖片參考：http://imgcld.yimg.com/8/n/HA06828592/o/701108150058213873443320.jpg
360 / 3 = 120 <-- ecterior angle
180 - 120 = 60 <-- interior angle
60 / 120 = 0.5 <-- interior angle / ecterior angle = 3 times

圖片參考：http://imgcld.yimg.com/8/n/HA06828592/o/701108150058213873443331.jpg
360 / 4 = 90
180 - 90 = 90
90 / 90 = 1

五边形 ： 360 / 5 = 72
180 - 72 = 108
108 / 72 = 1.5

六边形：360 / 6 = 60
180 - 60 = 120
120 / 60 = 2

七边形：360 / 7 = 51.42
180 - 51.42 = 128.58
128.58 / 51.42 = 2.5

八边形：360 / 8 = 45 <-- ecterior angle
180 - 45 = 135 <-- interior angle
135 / 45 = 3 <-- interior angle / ecterior angle = 3 times

(a) Find the size of each exteriror angle. 45
(b) Find the size of each interior angle.135
(c) Name the regular polygon. Octagon


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