Page 106 - Engineering

‫ﺍﳌﺜﻠﺜﺎﺕ ‪٩٣‬‬

‫‪A‬‬
‫‪75°‬‬

‫‪y° x°‬‬
‫‪50° z° 110°‬‬

‫‪BD‬‬ ‫‪C‬‬

‫اﻟﺤﻞ‪ :‬اﻹﺟﺎﺑﺔ ﻫﻲ )د(‪ :‬ﲟﺎ أن ‪ z + 110 = 180‬ﻓﺈن ‪ .z = 70°‬وﲟﺎ أن ﳎﻤﻮع‬

‫زواﻳﺎ ‪ △ABD‬ﻳﺴﺎوي ‪ 180°‬ﻓﺈن ‪ .y = 180 − (50 + 70) = 60°‬إذن‪،‬‬

‫‪.x = 180 − (75 + y) = 180 − (75 + 60) = 45°‬‬

‫)‪ [Aust.MC 1991] (٢١‬ﰲ اﻟﺸﻜﻞ اﳌﺮﻓﻖ‪،PRQ = 40° ،PR = QR ،‬‬

‫‪ .PTU = 25°‬ﻣﺎ ﻗﻴﺎس ‪ RST‬؟‬

‫)د( ‪140°‬‬ ‫)ج( ‪135°‬‬ ‫)ب( ‪125°‬‬ ‫)أ( ‪115°‬‬

‫‪R‬‬

‫‪40°‬‬

‫‪U‬‬

‫‪S‬‬
‫‪25°‬‬

‫‪P QT‬‬

‫اﻟﺤﻞ‪ :‬اﻹﺟﺎﺑﺔ ﻫﻲ )ج(‪ :‬ﲟﺎ أن ‪ PR = QR‬ﻓﺈن ‪.RQP = RPQ = 70°‬‬
‫و‪‬ﺬا ﻓﺈن ‪ RQT = 180 − 70 = 110°‬وﻳﻜﻮن‬

‫‪QST = 180 − (110 + 25) = 45°‬‬

‫إذن‪.RST = 180° − 45° = 135° ،‬‬