IDNStudy.com, ang iyong gabay para sa maaasahan at mabilis na mga sagot. Magtanong at makatanggap ng maaasahang sagot mula sa aming dedikadong komunidad ng mga eksperto.
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.
Salamat sa iyong presensya. Patuloy na magbahagi ng impormasyon at karanasan. Ang iyong kaalaman ay mahalaga sa ating komunidad. IDNStudy.com ang iyong mapagkakatiwalaang kasama para sa lahat ng iyong mga katanungan. Bisitahin kami palagi.