Question : In $ riangle {PQR}, {PN}$ is the median on ${QR}$. If ${PN}={QN}$, then what is the value of $\angle {QPR}$?
Option 1: $90^\circ$
Option 2: $80^\circ$
Option 3: $60^\circ$
Option 4: $75^\circ$

Question

Question : In $ riangle {PQR}, {PN}$ is the median on ${QR}$. If ${PN}={QN}$, then what is the value of $\angle {QPR}$?

Option 1: $90^\circ$

Option 2: $80^\circ$

Option 3: $60^\circ$

Option 4: $75^\circ$

Team Careers360 · Accepted Answer

Correct Answer: $90^\circ$

Solution :
In $ riangle PQR$, PN is the median.
So, QN = NR
and PN = QN (given)
In $ riangle PQN$
PN = QN
Let $\angle QPN=\angle NQP = heta$
Similarly, In $ riangle PNR$
PN = NR
Let $\angle NPR = \angle NRP = \alpha$
$ herefore QPR= heta + \alpha$
In $ riangle PQR$,
$\angle QPR+\angle QRP +\angle RQP=180^\circ$
⇒ $( heta+\alpha)+ heta + \alpha=180^\circ$
⇒ $2( heta+\alpha)=180^\circ$
⇒ $( heta+\alpha)=90^\circ$
So, $\angle QPR = 90^\circ$
Hence, the correct answer is $90^\circ$.

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Question : In △PQR,PN is the median on QR. If PN=QN, then what is the value of ∠QPR?Option 1: 90∘Option 2: 80∘Option 3: 60∘Option 4: 75∘

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Question : In $△ P Q R, P N$ is the median on $Q R$ . If $P N = Q N$ , then what is the value of $∠ Q P R$ ?
Option 1: $90^{\circ}$
Option 2: $80^{\circ}$
Option 3: $60^{\circ}$
Option 4: $75^{\circ}$