Question
Download Solution PDF△XYZ এর ∠XYZ এবং ∠XZY এর অভ্যন্তরীণ দ্বিখণ্ডক একে অপরের সাথে k তে মিলিত হয়। যদি ∠YKZ = 112° হয়, তবে ∠YXZ এর মান নির্ণয় করুন।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFপ্রদত্ত:
∠YKZ = 112°
সূত্র:
ত্রিভুজের তিনটি কোণের সমষ্টি হল 180°
যেহেতু, K হল অন্তঃকেন্দ্র তাই ∠YKZ = 90° + XYXZ/2
গণনা:
△ YKZ তে
∠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°
যেহেতু আমরা জানি
∠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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