[問題]考古題From14 sec3 DS-Q25

[凱薩琳]

If P is a polygon with all sides of equal measure and no line containing a side of the polygon contains a point in the interior of the polygon, hoe many sides does P have?

(1)Each interior abgle measures 135
(2)The sum of the measures of the interior angles is 1,080

Ans:D
看不太懂題目的說...

[singingsong]

題目大概是說:假如p是一個每一邊都一樣長的多邊形,每一個邊和其他的邊都只交逢于一點,那p是幾邊的多邊形?
根據題目的條件,p是一個正多邊形,假設p有n個邊
正多邊形的內角合=(n-2)*180
由條件2帶入公式可推知n等於多少,
而條件1 135*n=(n-2)*180也可推知n等於多少
所以條件1 & 2 均可單獨成立,選D

[凱薩琳]

感謝回答