This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Huu hapa ni utatuzi wa swali hilo: Step 1: Andika fomula ya idadi ya diagonals na uanzishe mlinganyo. Acha n iwe idadi ya pande za poligoni. Idadi ya diagonals, D, inatolewa na fomula: D = (n(n-3))/(2) Kutokana na swali, idadi ya diagonals ni mara tatu ya idadi ya pande: D = 3n Sasa, weka fomula hizi mbili sawa: (n(n-3))/(2) = 3n Step 2: Tatua mlinganyo ili kupata idadi ya pande, n. Zidisha pande zote mbili kwa 2: n(n-3) = 6n Panua upande wa kushoto: n^2 - 3n = 6n Peleka maneno yote upande mmoja: n^2 - 3n - 6n = 0 n^2 - 9n = 0 Toa n kama kigezo cha kawaida: n(n-9) = 0 Hii inatoa suluhisho mbili: n=0 au n=9. Kwa kuwa poligoni haiwezi kuwa na pande 0, tunachukua n=9. Poligoni ina pande 9. Step 3: Tafuta kipimo cha kila pembe ya nje. Kwa poligoni ya kawaida yenye pande n, kipimo cha kila pembe ya nje hutolewa na fomula: Pembe ya nje = (360^)/(n) Badilisha n=9 kwenye fomula: Pembe ya nje = (360^)/(9) Pembe ya nje = 40^ Kipimo cha kila pembe ya nje ni: 40^ That's 2 down. 3 left today — send the next one.