Question
Download Solution PDFएक चतुर्भुज ABCD मध्ये, ∠C आणि ∠D चे दुभाजक E बिंदूवर भेटतात. जर ∠CED = 57° आणि ∠A = 47°, तर ∠B चे माप आहे:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिलेले आहे:
∠CED = 57° आणि ∠A = 47°
वापरलेली संकल्पना:
त्रिकोणाच्या सर्व कोनांची बेरीज = 180°
चौकोनाच्या सर्व कोनांची बेरीज = 360°
गणना:
ΔCED मध्ये, ∠CDE + ∠DCE + ∠CED = 180°
⇒ ∠D/2 + ∠C/2 + 57° = 180°
⇒ ∠D/2 + ∠C/2 = 180° - 57° = 123°
⇒ (∠D + ∠C)/2 = 123°
⇒ ∠D + ∠C = 123° × 2 = 246°
तसेच, ∠A + ∠B + ∠C + ∠D = 360°
⇒ 47° + ∠B + 246° = 360° [∵ ∠D + ∠C = 246°]
⇒ ∠B = 360° - 246° - 47° = 67°
∴ ∠B चे माप 67° आहे
Shortcut Trick ∠CED = 57° आणि ∠A = 47°
∠C आणि ∠D चे दुभाजक E बिंदूवर भेटतात
∠A + ∠B = 2 ∠CED
⇒ 47° + ∠B = 2 × 57°
⇒ ∠B = 114° - 47° = 67°
∴ ∠B चे माप 67° आहे
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