Page 48 - Engineering

‫ﺍﳌﺴﺘﻘﻴﻤﺎﺕ ﻭﺍﻟﺰﻭﺍﻳﺎ ‪٣٥‬‬

‫‪ .ɵy = 40°‬اﻵن‪ x + y + 80 = 180° ،‬ﻷ‪‬ﺎ زاوﻳﺔ ﻣﺴﺘﻘﻴﻤﺔ‪ .‬إذن‪.ɵx = 60° ،‬‬
‫و‪‬ﺬا ﻳﻜﻮن ‪.x − y = 20°‬‬

‫)‪ (٢٤‬ﰲ اﻟﺸﻜﻞ اﳌﺮﻓﻖ‬

‫‪HG‬‬ ‫‪CD‬‬
‫‪y°‬‬
‫‪10x ° 61°‬‬
‫‪75° 2y°‬‬ ‫‪7x °‬‬
‫‪AB‬‬
‫‪FE‬‬
‫)ب( ‪FCE = 60°‬‬
‫)أ( ‪GBC = 80°‬‬

‫)د( ‪HB CF‬‬ ‫)ج( ‪BG CF‬‬

‫اﻟﺤﻞ‪ :‬اﻹﺟﺎﺑﺔ ﻫﻲ )ج(‪ :‬ﻟﺪﻳﻨﺎ ‪.75 + y + 2y = 180°‬‬

‫وﻣﻦ ﰒ ﻓﺈن ‪ y = 35°‬وأن ‪ .2y = 70°‬أﻳﻀﺎً‪.10x + 7x + 61 = 180° ،‬‬
‫إذن‪ x = 7° ،‬وﻣﻦ ﰒ ﻓﺈن ‪ .10x = 70°‬ﻣﻦ ذﻟﻚ ﳒﺪ أن ‪ 2y = 10x‬وﳘﺎ‬

‫زاوﻳﺘﺎن ﺗﺒﺎدﻟﻴﺘﺎن داﺧﻠﻴﺎً‪ .‬إذن‪.BG CF ،‬‬

‫)‪ (٢٥‬ﰲ اﻟﺸﻜﻞ اﳌﺮﻓﻖ‪ BE ،AB CD ،‬ﻳﻨﺼﻒ ‪ CE ،ABC‬ﻳﻨﺼﻒ‬

‫‪ .DCB‬ﻗﻴﺎس ‪ BEC‬ﻳﺴﺎوي‬

‫)د( ‪100°‬‬ ‫)ج( ‪95°‬‬ ‫)ب( ‪90°‬‬ ‫)أ( ‪80°‬‬

‫‪B‬‬ ‫‪A‬‬
‫‪E‬‬ ‫‪D‬‬

‫‪C‬‬