Question
Download Solution PDFएक चक्रीय चतुर्भुज ABCD की भुजाएँ AB और DC को E पर मिलने के लिए बढ़ाया गया है और भुजाओं AD और BC को F पर मिलने के लिए बढ़ाया गया है। यदि ∠ADC = 78° और ∠BEC = 52° है, तो ∠AFB की माप क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
∠ADC = 78° और ∠BEC = 52°
अवधारणा:
चक्रीय चतुर्भुज में सम्मुख कोणों के एक युग्म का योग का 180° होता है।
गणना:
अब, चतुर्भुज ABCD में,
∠ADC + ∠ABC = 180° (सम्मुख कोणों का योग 180° होता है)
⇒ ∠ABC = 180° - 78° = 102°
∠EBC = 180° - 102° = 78° [रैखिक युग्म]
ΔBEC में,
∠BEC + ∠EBC + ∠BCE = 180°
⇒ 52° + 78° + ∠BCE = 180°
⇒ ∠BCE = 180° - 130° = 50°
⇒ ∠BCE = ∠DCF = 50° (शीर्षाभिमुख कोण)
∠ADE + ∠FDC = 180° [रैखिक युग्म]
⇒ ∠FDC = 180° - ∠ADE = 180° - 78° = 102°
ΔDCF में,
∠FDC + ∠DCF + ∠DFC = 180°
102 + 50 + ∠DFC = 180°
∠DFC = 180° - 152° = 28°
∠DFC = ∠AFB = 28°
∴ ∠AFB की माप 28° है।
Last updated on Jul 8, 2025
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