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標題: 問功課---F.2 maths [打印本頁]

作者: ZZdaphne 時間: 10-5-23 00:54 標題: 問功課---F.2 maths

find the number of sides of a regular polygon if each of its interior angle is 22 degree more than that of a nonagon.

ans:20

how to prove that? thanks all!!!

作者: 88muimui 時間: 10-5-23 09:12

可以上YAHOO 知識問下

原帖由 ZZdaphne 於 10-5-23 00:54 發表
find the number of sides of a regular polygon if each of its interior angle is 22 degree more than that of a nonagon.

ans:20

how to prove that? thanks all!!!

作者: BillyM 時間: 10-5-23 10:44

size of each int angle of a nonagon:

(9-2) x 180 / 9 = 140

size of each int angle of this unknown n-gon:

140 + 22 = 162

sum of all int angles of this n-gon:

(n - 2) x 180 = 162 x n

n = 20

== OR ==

size of each ext angle of this n-gon:

180 - 162 = 18

=> 18n = 360

n = 20

原帖由 ZZdaphne 於 10-5-23 00:54 發表
find the number of sides of a regular polygon if each of its interior angle is 22 degree more than that of a nonagon.

ans:20

how to prove that? thanks all!!!

作者: ZZdaphne 時間: 10-5-23 12:36

原帖由 BillyM 於 10-5-23 10:44 發表
size of each int angle of a nonagon:

(9-2) x 180 / 9 = 140

size of each int angle of this unknown n-gon:

140 + 22 = 162

sum of all int angles of this n-gon:

(n - 2) x 180 = 162 x n

n = 20

== O ...

thanks

原來昨晚我們理解錯了呢句:
interior angle is 22 degree more than that of a nonagon.
一起身再諗,攪拈了.

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