Question
Download Solution PDF△PQR में, भुजा PQ और PR को E और F तक इस प्रकार खिंचा गया है कि ∠Q और ∠R के बाहरी कोण द्विभाजक बिंदु k पर मिलते हैं। यदि ∠QPR = 110°, तो ∠QKR = ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया है:
∠QPR = 110°
सूत्र:
एक त्रिभुज के सभी तीन कोणों का योगफल 180° होता है।
∠QKR = 90° - ∠QPR/2
गणना:
∠RQK = (180° - ∠PQR)/2
∠QRK = (180° - ∠PRQ)/2
△QKR में
∠RQK + ∠QRK + ∠QKR = 180°
⇒ [(180° - ∠PQR)/2] + [(180° - ∠PRQ)/2] + ∠QKR = 180°
⇒ 90° - [∠PQR/2] + 90 – [∠PRQ/2] + ∠QKR = 180°
⇒ 180 – [(∠PQR + ∠PRQ)/2] + ∠QKR = 180
⇒ ∠QKR = (∠PQR + ∠PRQ)/2
⇒ 2∠QKR = ∠PQR + ∠PRQ
⇒ 2∠QKR = 180° - ∠QPR
⇒ 2∠QKR = 180° - 110
⇒ ∠QKR = 70/2
∴ ∠QKR = 35°
लघु विधि:
यहाँ, K ΔPQR का वाह्य-केंद्र है, इस प्रकार ∠QKR = 90° - (∠QPR/2)
∠QKR = 90° - 110°/2
∴ ∠QKR = 90° - 55° = 35°
Last updated on Jul 10, 2025
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