In ΔPQR, PN is the median on QR. If PN = QN, then what is the value of ∠QPR?
Answer & explanation
Correct answer: option 1
In \(\Delta \)PQR, PN is the median,
QN = NR
PN = QN
In \(\Delta \)PQN
PN = QN
\(\angle\)QPN = \(\angle\)NQP = \(\theta \)
Similarly, In \(\Delta \)PNR
PN = NR
\(\angle\)PNR = \(\angle\)NRP = \(\alpha \)
Therefore, \(\angle\)QPR = \(\theta \) + \(\alpha \)
In \(\Delta \)PQR, apply Angle sum property
\(\angle\)QPR + \(\angle\)QRP + \(\angle\)RQP = 180
(\(\theta \) + \(\alpha \)) +\(\theta \) + \(\alpha \) = 180
2(\(\theta \) + \(\alpha \)) = 180
(\(\theta \) + \(\alpha \)) = 90
Therefore, \(\angle\)QPR = \({90}^\circ\).