Question
Download Solution PDF△XYZ च्या ∠XYZ व ∠XZY चा आंतरिक दुभाजक k जवळ एकमेकांना मिळतात. जर ∠YKZ = 112° असेल, तर ∠YXZ = ______.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिलेले:
∠YKZ = 112°
सूत्र:
त्रिकोणाच्या तिन्ही कोनांच्या मापांची बेरीज 180° असते.
K हे आंतरकेंद्र आहे, म्हणून ∠YKZ = 90° + ∠YXZ/2
पडताळा:
△YKZ मध्ये
∠XYZ/2 + ∠XZY/2 + ∠YKZ = 180°
⇒ ∠XYZ/2 + ∠XZY/2 + 112° = 180°
⇒ ∠XYZ/2 + ∠XZY/2 = 180° - 112°
⇒ ∠XYZ + ∠XZY = 2 × 68°
⇒ ∠XYZ + ∠XZY = 136°
आपल्याला माहीत आहे,की
∠YXZ + ∠XYZ + ∠XZY = 180°
⇒ ∠YXZ + 136° = 180°
⇒ ∠YXZ = 180° - 136°
∴ ∠YXZ = 44°
∠YKZ = 90° + ∠YXZ /2
⇒ 112° = 90° + ∠YXZ/2
⇒ ∠YXZ/2 = 112° - 90°
⇒ ∠YXZ = 22° × 2
∴ ∠YXZ = 44°
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