Question
Download Solution PDFदिलेल्या त्रिकोणामध्ये, CD हा ∠BCA चा दुभाजक आहे. CD = DA. जर ∠BDC = 76°, तर ∠CBD चे अंश माप काय आहे?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिलेले आहे:
CD हा ∠BCA चा दुभाजक आहे.
CD = DA
∠BDC = 76°
वापरलेली संकल्पना:
समद्विभुज त्रिकोणाचे दोन कोन, समान बाजूंच्या विरुद्ध, मोजमापाने समान असतात.
कोन बेरीज गुणधर्म = त्रिकोणाच्या तीनही कोनांची बेरीज 180° आहे.
गणना:
ABC त्रिकोणामध्ये,
CD हा ∠BCA चा दुभाजक आहे.
⇒ ∠BCD = ∠DCA = θ
पासून, CD = DA [दिलेले]
⇒ ∠DCA = ∠CAD = θ
⇒ ∠BDC = 76° [दिलेले]
⇒ ∠BDC = ∠DCA + ∠CAD
⇒ θ + θ = 76°
⇒ 2θ = 76°
⇒ θ = 38°
CBD त्रिकोणामध्ये,
∠BCD + ∠CDB + ∠CBD = 180°
⇒ θ + 76° + ∠CBD = 180°
⇒ 38° + 76° + ∠CBD = 180°
⇒ ∠CBD = 180° - 114°
⇒ ∠CBD = 66°
∴ पर्याय 4 हे योग्य उत्तर आहे.
Last updated on Jun 13, 2025
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