IDNStudy.com, kung saan nagtatagpo ang mga eksperto para sagutin ang iyong mga tanong. Magtanong at makakuha ng detalyadong sagot mula sa aming komunidad ng mga eksperto na may kaalaman.
Sagot :
Given:
Interior angle of a polygon - [tex] 144^{o}
Find:
Number of diagonals the polygon have
Solution:
(Let us settle with the degrees later.)
Interior angle = [tex] \frac{180 (n-2)}{n) [/tex]
144 = [tex] \frac{180 (n-2)}{n} [/tex]
144n = 180 n - 360
144n - 180n = 180n - 180n - 360
[tex] \frac{-36n = -360}{-36} [/tex]
n = 10
n = 10, that means that the polygon is a 10-sided polygon or DECAGON.
The remaining problem is its number of diagonals.
Number of diagonals = [tex] \frac{n(n-3)}{2} [/tex]
= [tex] \frac{ 10(10 - 3)}{2} [/tex]
= [tex] \frac{10 (7)}{2} [/tex]
= [tex] \frac{70}{2} [/tex]
= 35
Answer:
The regular polygon that has an interior angle of 144 degrees has 35 diagonals.
Interior angle of a polygon - [tex] 144^{o}
Find:
Number of diagonals the polygon have
Solution:
(Let us settle with the degrees later.)
Interior angle = [tex] \frac{180 (n-2)}{n) [/tex]
144 = [tex] \frac{180 (n-2)}{n} [/tex]
144n = 180 n - 360
144n - 180n = 180n - 180n - 360
[tex] \frac{-36n = -360}{-36} [/tex]
n = 10
n = 10, that means that the polygon is a 10-sided polygon or DECAGON.
The remaining problem is its number of diagonals.
Number of diagonals = [tex] \frac{n(n-3)}{2} [/tex]
= [tex] \frac{ 10(10 - 3)}{2} [/tex]
= [tex] \frac{10 (7)}{2} [/tex]
= [tex] \frac{70}{2} [/tex]
= 35
Answer:
The regular polygon that has an interior angle of 144 degrees has 35 diagonals.
Ang iyong aktibong pakikilahok ay mahalaga sa amin. Magpatuloy sa pagtatanong at pagbibigay ng mga sagot. Sama-sama tayong lumikha ng isang komunidad ng karunungan. May mga katanungan ka? Ang IDNStudy.com ang may sagot. Salamat sa iyong pagbisita at sa muling pagkikita.