Page 50 - Engineering

‫ﺍﳌﺴﺘﻘﻴﻤﺎﺕ ﻭﺍﻟﺰﻭﺍﻳﺎ ‪٣٧‬‬

‫)‪ [Gauss 2010] (٢٨‬ﰲ اﻟﺸﻜﻞ اﳌﺮﻓﻖ‪ PQR ،‬ﻣﺴﺘﻘﻴﻢ‪ .‬ﻣﺎ ﻗﻴﻤﺔ ‪ x‬؟‬

‫)د( ‪75°‬‬ ‫)ج( ‪69°‬‬ ‫)ب( ‪64°‬‬ ‫)أ( ‪54°‬‬

‫‪x°‬‬ ‫‪R‬‬
‫‪42° x °‬‬
‫‪PQ‬‬

‫اﻟﺤﻞ‪ :‬اﻹﺟﺎﺑﺔ ﻫﻲ )ج(‪ :‬ﻟﺪﻳﻨﺎ‬

‫‪x + x + 42 = 180°‬‬

‫‪2x = 138°‬‬

‫‪x = 69°.‬‬

‫)‪ [MAΘ 2011 ] (٢٩‬اﻟﺰاوﻳﺘﺎن ‪ A‬و ‪ B‬ﻣﺘﻜﺎﻣﻠﺘﺎن واﻟﺰاوﻳﺘﺎن ‪ B‬و ‪C‬‬

‫ﻣﺘﻜﺎﻣﻠﺘﺎن أﻳﻀﺎً‪ .‬إذا ﻛﺎن ‪ A = (3x + 16)°‬و ‪ C = (5x − 24)°‬ﻓﻤﺎ‬

‫ﻗﻴﺎس اﻟﺰاوﻳﺔ ‪ B‬؟‬

‫)د( ‪134°‬‬ ‫)ج( ‪104°‬‬ ‫)ب( ‪84°‬‬ ‫)أ( ‪70°‬‬

‫اﻟﺤﻞ‪ :‬اﻹﺟﺎﺑﺔ ﻫﻲ )ج(‪ :‬ﻟﺪﻳﻨﺎ‬

‫‪A + B = 180°‬‬

‫‪3x + 16 + B = 180‬‬

‫‪(١) B = 164 − 3x‬‬

‫أﻳﻀﺎً‪،‬‬

‫‪B + C = 180°‬‬

‫‪B + 5x − 24 = 180‬‬

‫‪(٢) B = 204 − 5x‬‬