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 ufumbuzi wa swali lako: 4. Katika mchoro hapa chini, arc UVW = arc WXY, Chord WX = Chord XY na UVW = 110^. Tafuta: Hatua ya 1: Tafuta vipimo vya arc kutokana na pembe na kodi zilizotolewa. • Pembe UVW = 110^ ni pembe iliyoandikwa kwenye duara. Inaunda arc UW (arc kubwa isiyo na V). Hivyo, m(UW)_kubwa = 2 × UVW = 2 × 110^ = 220^. • Arc ndogo UW (inayopitia V) ni 360^ - 220^ = 140^. Hivyo, m(UVW) = 140^. • Tunapewa arc(UVW) = arc(WXY). Hivyo, m(WXY) = 140^. • Tunapewa Chord WX = Chord XY. Hii inamaanisha arc zao zinazofanana ni sawa: m(WX) = m(XY). • Kutoka m(WXY) = m(WX) + m(XY), tunapata: 140^ = m(WX) + m(WX) = 2 × m(WX). Hivyo, m(WX) = (140^)/(2) = 70^. Na m(XY) = 70^. • Jumla ya arc zote kwenye duara ni 360^. m(UV) + m(VW) + m(WX) + m(XY) + m(YU) = 360^. Tunajua m(UV) + m(VW) = m(UVW) = 140^. Hivyo, 140^ + 70^ + 70^ + m(YU) = 360^. 280^ + m(YU) = 360^. m(YU) = 360^ - 280^ = 80^. Sasa tuna vipimo vya arc: m(WX) = 70^ m(XY) = 70^ m(YU) = 80^ m(UVW) = 140^ Hatua ya 2: Tafuta pembe zinazohitajika. a) WUY Pembe WUY inaunda arc WY. m(WY) = m(WX) + m(XY) = 70^ + 70^ = 140^. WUY = (1)/(2) m(WY) = (1)/(2) × 140^ = 70^ WUY = 70^ b) WUX Pembe WUX inaunda arc WX. WUX = (1)/(2) m(WX) = (1)/(2) × 70^ = 35^ WUX = 35^ c) XWY Pembe XWY inaunda arc XY. XWY = (1)/(2) m(XY) = (1)/(2) × 70^ = 35^ XWY = 35^ d) YXW Pembe YXW inaunda arc YW (arc isiyo na X). m(YW) = m(YU) + m(UVW) = 80^ + 140^ = 220^$. YXW = (1)/(2) m(YW) = (1)/(2) × 220^ = 110^ YXW = 110^ Tuma swali linalofuata 📸