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
Ili kutatua swali hili, tutatumia formula ya pembe ya ndani ya poligoni ya kawaida. Step 1: Andika formula ya pembe ya ndani ya poligoni ya kawaida. Pembe ya ndani ya poligoni ya kawaida yenye n pande hutolewa na formula: I = ((n-2) × 180^)/(n) Step 2: Andika milinganyo ya pembe za ndani kwa poligoni mbili. Kwa poligoni ya kwanza yenye 3y pande (n_1 = 3y), pembe yake ya ndani ni: I_1 = ((3y - 2) × 180^)/(3y) Kwa poligoni ya pili yenye y pande (n_2 = y), pembe yake ya ndani ni: I_2 = ((y - 2) × 180^)/(y) Step 3: Tengeneza mlinganyo kulingana na masharti yaliyotolewa. Imesemwa kuwa pembe ya ndani ya poligoni ya kwanza inazidi pembe ya ndani ya poligoni ya pili kwa 40^. Hivyo: I_1 - I_2 = 40^ ((3y - 2) × 180)/(3y) - ((y - 2) × 180)/(y) = 40 Step 4: Tatua mlinganyo ili kupata thamani ya y. Gawanya mlinganyo mzima kwa 20: ((3y - 2) × 9)/(3y) - ((y - 2) × 9)/(y) = 2 Rahisisha: (3(3y - 2))/(y) - (9(y - 2))/(y) = 2 Zidisha pande zote mbili kwa y ili kuondoa denominator: 3(3y - 2) - 9(y - 2) = 2y Panua mabano: 9y - 6 - 9y + 18 = 2y Unganisha vigezo vinavyofanana: 12 = 2y Gawanya kwa 2: y = (12)/(2) y = 6 Thamani ya y ni: 6 That's 2 down. 3 left today — send the next one.