In ΔPQR, PN is the median on QR. If PN = QN, then what is the value of ∠QPR?

90 degree

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 = \({90}^\circ\).