Page 38 - Engineering

‫ﺍﳌﺴﺘﻘﻴﻤﺎﺕ ﻭﺍﻟﺰﻭﺍﻳﺎ ‪٢٥‬‬

‫‪ . 8r + 10° = 90°‬وﻣﻦ ذﻟﻚ ﻳﻜﻮن ‪ .r = 10°‬و‪‬ﺬا ﻓﺈن‬
‫‪ .A = 2r + 5 = 25°‬وأﺧﲑاً‪.B = 90° − A = 90° − 25° = 65° ،‬‬

‫)‪ (٥‬ﰲ اﻟﺸﻜﻞ اﳌﺮﻓﻖ‪ MNL = 73° ،‬و ‪ KNM ،INJ = 41°‬و ‪INL‬‬
‫ﻣﺴﺘﻘﻴﻤﺎن‪ .‬ﻣﺎ ﻗﻴﺎس اﻟﺰاوﻳﺔ ‪ JNK‬؟‬

‫‪M‬‬
‫‪I‬‬

‫‪JN‬‬

‫‪L‬‬
‫‪K‬‬

‫)د( ‪52°‬‬ ‫)ج( ‪42°‬‬ ‫)ب( ‪32°‬‬ ‫)أ( ‪22°‬‬

‫اﻟﺤﻞ‪ :‬اﻹﺟﺎﺑﺔ ﻫﻲ )ب(‪ INK = MNL = 73° :‬ﺑﺎﻟﺘﻘﺎﺑﻞ ﺑﺎﻟﺮأس‪ .‬إذن‪،‬‬

‫‪.JNK = INK − INJ = 73° − 41° = 32°‬‬

‫)‪ (٦‬ﰲ اﻟﺸﻜﻞ اﳌﺮﻓﻖ‪ A ،‬ﻧﻘﻄﺔ واﻗﻌﺔ ﻋﻠﻰ اﳌﺴﺘﻘﻴﻢ ‪ EB‬واﻟﺰاوﻳﺘﺎن ‪ BAC‬و‬
‫‪ EAD‬ﻣﺘﻄﺎﺑﻘﺘﺎن‪ .‬ﻣﺎ ﻗﻴﺎس اﻟﺰاوﻳﺔ ‪ DAC‬؟‬

‫‪D‬‬ ‫‪C‬‬
‫‪(5x + 7)°‬‬ ‫‪(3x + 23)°‬‬

‫‪EA‬‬ ‫‪B‬‬

‫)د( ‪95°‬‬ ‫)ج( ‪90°‬‬ ‫)ب( ‪86°‬‬ ‫)أ( ‪77°‬‬

‫اﻟﺤﻞ‪ :‬اﻹﺟﺎﺑﺔ ﻫﻲ )ب(‪ :‬ﲟﺎ أن ‪ BAC = EAD‬ﻓﺈن‬