Question
Download Solution PDFএকটি বৃত্তীয় চতুর্ভুজ ABCD এর AB এবং DC বাহুগুলি E তে মিলিত হয় এবং AD এবং BC বাহুগুলি F -এ মিলিত হয়। যদি ∠ADC = 78° এবং ∠BEC = 52° হয়, তাহলে ∠AFB এর পরিমাপ হল:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFদেওয়া হয়েছে:
∠ADC = 78° এবং ∠BEC = 52°
ধারণা:
একটি বৃত্তীয় চতুর্ভুজের একজোড়া বিপরীত কোণের সমষ্টি 180°
হিসাব:
এখন, চতুর্ভুজ ABCD-তে,
∠ADC + ∠ABC = 180° (বিপরীত কোণের যোগফল 180°)
⇒ ∠ABC = 180° - 78° = 102°
∠EBC = 180° - 102° = 78° [রৈখিক জোড়া]
ΔBEC-তে,
∠BEC + ∠EBC + ∠BCE = 180°
⇒ 52° + 78° + ∠BCE = 180°
⇒ ∠BCE = 180° - 130° = 50°
⇒ ∠BCE = ∠DCF = 50° (বিপ্রতীপ কোণ)
∠ADE + ∠FDC = 180° [রৈখিক জোড়া]
⇒ ∠FDC = 180° - ∠ADE = 180° - 78° = 102°
ΔDCF-তে,
∠FDC + ∠DCF + ∠DFC = 180°
102 + 50 + ∠DFC = 180°
∠DFC = 180° - 152° = 28°
∠DFC = ∠AFB = 28°
∴ ∠AFB এর পরিমাপ 28°.
Last updated on Jun 13, 2025
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