Răspuns: Ai rezolvarea mai jos
Explicație pas cu pas:
(*^_^*) Buna!
Poligonul cu 9 laturi se numește eneagon.
[tex]\color{CC0000}\boxed{\bf Nr~diagonalelor~unui~poligon: \dfrac{(n-3)\cdot n}{2};~ n-nr~de~ laturi}[/tex]
[tex]\color{forestgreen}\bf \boxed{\bf Masura~unui~unghi~poligon~regulat: \dfrac{(n-2)\cdot 180^{\circ}}{n};n-nr~ de~ laturi}[/tex]
[tex]\bf Nr~diagonalelor~poligonului: \dfrac{(9-3)\cdot 9}{2}=\dfrac{6\cdot 9}{2}=\boxed{\bf 27~diagonale}[/tex]
[tex]\bf Masura~unui~unghi: \dfrac{(9-2)\cdot 180^{\circ}}{9}=\dfrac{7\cdot 180^{\circ}}{9}=\boxed{\bf 140^{\circ}}[/tex]
[tex]\bf \measuredangle U_{1}+ \measuredangle U_{2}+ \measuredangle U_{3}+u_{4}+ \measuredangle U_{5}+ \measuredangle U_{6}+ \measuredangle U_{7}+ \measuredangle U_{8}+ \measuredangle U_{9}=1260^{\circ}[/tex]
[tex]\bf~~[/tex]
- Unghiuri consecutive cate 2 sunt
∡U₁ + ∡U₂ → 140° + 140° = 280°
∡U₂ + ∡U₃ → 140° + 140° = 280°
∡U₃ + ∡U₄ → 140° + 140° = 280°
............................................................
∡U₉ + ∡U₁ → 140° + 140° = 280°
- Unghiuri consecutive cate 3 sunt
∡U₁ + ∡U₂ + ∡U₃ → 140° + 140° + 140° = 420°
∡U₂ + ∡U₃ + ∡U₄ → 140° + 140° + 140° = 420°
∡U₃ + ∡U₄ + ∡U₅ → 140° + 140° + 140° = 420°
....................................................................................
∡U₉ + ∡U₁ + ∡U₂ → 140° + 140° + 140° = 420°
[tex]\bf~~~[/tex]
PS: Daca esti pe telefon, te rog sa glisezi spre dreapta pentru a vedea rezolvarea completa
#copaceibrainly
