Question
Download Solution PDF∠XYZ ന്റെ ആന്തരിക സമഭാജിയും, △ XYZ ന്റെ ∠XZY യും പരസ്പരം k എന്ന ബിന്ദുവിൽ യോജിക്കുന്നു. ∠YKZ = 112° ആണെങ്കിൽ, ∠YXZ എന്തിനോട് തുല്യമാണ്?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFതന്നിരിക്കുന്നത്:
∠YKZ = 112°
സൂത്രവാക്യം:
ഒരു ത്രികോണത്തിന്റെ 3 കോണുകളുടെയും തുക 180°
K ആന്തര കേന്ദ്രത്തിലായതിനാൽ, ∠YKZ = 90° + ∠YXZ/2
കണക്കുകൂട്ടൽ:
△YKZ ൽ
∠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°
നമുക്കറിയാവുന്നത് പോലെ
∠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°
Last updated on Jul 22, 2025
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