Question
Download Solution PDFदिए गए त्रिभुज में, CD, ∠BCA का समद्विभाजक है। CD = DA हैं। यदि ∠BDC = 76° है, तो ∠CBD का डिग्री माप क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
CD, ∠BCA का समद्विभाजक है।
CD = DA
∠BDC = 76°
प्रयुक्त अवधारणा:
एक समद्विबाहु त्रिभुज के दो कोण, जो दो बराबर भुजाओं के विपरीत हों, माप में समान होते हैं।
कोण योग गुणधर्म = त्रिभुज के तीनों कोणों का योग 180° होता है।
गणना:
त्रिभुज ABC में,
CD, ∠BCA का समद्विभाजक है।
⇒ ∠BCD = ∠DCA = θ
चूँकि, CD = DA [दिया गया है]
⇒ ∠DCA = ∠CAD = θ
⇒ ∠BDC = 76° [दिया गया है]
⇒ ∠BDC = ∠DCA + ∠CAD
⇒ θ + θ = 76°
⇒ 2θ = 76°
⇒ θ = 38°
त्रिभुज CBD में,
∠BCD + ∠CDB + ∠CBD = 180°
⇒ θ + 76° + ∠CBD = 180°
⇒ 38° + 76° + ∠CBD = 180°
⇒ ∠CBD = 180° - 114°
⇒ ∠CBD = 66°
∴ सही उत्तर विकल्प 4 है।
Last updated on Jun 11, 2025
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