Question
Download Solution PDFचक्रीय चौकोन ABCD च्या बाजू AB आणि DC ला बिंदू E वर आणि बाजू AD आणि BC ला बिंदू F वर मिळतात. जर ∠ADC = 78° आणि ∠BEC = 52° असेल, तर ∠AFB चे माप काय असेल?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिलेले आहे:
∠ADC = 78° आणि ∠BEC = 52°
संकल्पना:
चक्रीय चौकोनाच्या विरुद्ध कोनांची बेरीज 180° असते.
गणना:
आता, चौकोन ABCD मध्ये,
∠ADC + ∠ABC = 180° (विरुद्ध कोनांची बेरीज 180°)
⇒ ∠ABC = 180° - 78° = 102°
∠EBC = 180° - 102° = 78° [रेषीय जोडी]
ΔBEC मध्ये,
∠BEC + ∠EBC + ∠BCE = 180°
⇒ 52° + 78° + ∠BCE = 180°
⇒ ∠BCE = 180° - 130° = 50°
⇒ ∠BCE = ∠DCF = 50° (विरुद्ध कोन)
∠ADE + ∠FDC = 180° [रेषीय जोडी]
⇒ ∠FDC = 180° - ∠ADE = 180° - 78° = 102°
ΔDCF मध्ये,
∠FDC + ∠DCF + ∠DFC = 180°
102° + 50° + ∠DFC = 180°
∠DFC = 180° - 152° = 28°
∠DFC = ∠AFB = 28°
म्हणून, ∠AFB चे माप 28° आहे.
Last updated on Jul 7, 2025
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