Question:
In a \(\Delta PQR\), side QR is extended to point ‘E’, such that \(\angle PRE = 127^\circ\). If \(\angle QPR = (3/2) \times \angle PQR\), then find the value of \(\angle QPR\).
एक \(\Delta PQR\) में, भुजा QR को बिंदु ‘E’ तक बढ़ाया जाता है, जिससे \(\angle PRE = 127^\circ\) बनता है। यदि \(\angle QPR = (3/2) \times \angle PQR\) है, तो \(\angle QPR\) का मान ज्ञात कीजिए।
Options:
- 54.6°
- 60°
- 76.2°
- 72°
- 54.6°
- 60°
- 76.2°
- 72°
Correct Answer: c)
Explanation:
By the exterior angle theorem, \(\angle PRE = \angle QPR + \angle PQR\).
\(127^\circ = \dfrac{3}{2}\angle PQR + \angle PQR = \dfrac{5}{2}\angle PQR\).
\(\angle PQR = \dfrac{127 \times 2}{5} = 50.8^\circ\).
\(\angle QPR = \dfrac{3}{2} \times 50.8^\circ = 76.2^\circ\).
त्रिभुज के बहिष्कोण प्रमेय के अनुसार: \(\angle PRE = \angle QPR + \angle PQR\)।
\(127^\circ = \dfrac{5}{2}\angle PQR \implies \angle PQR = 50.8^\circ\)।
\(\angle QPR = \dfrac{3}{2} \times 50.8^\circ = 76.2^\circ\)।