In \(\triangle PQR\), QT is perpendicular to PR, where T lies on PR. S is a point on QR such that \(\angle TQR=34^\circ\) and \(\angle SPR=45^\circ\). If \(\angle PSQ=x^\circ\), what is the value of \(x\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 101
The angles of a triangle add up to \(180^\circ\), and an exterior angle of a triangle equals the sum of the two interior opposite angles.
In right \(\triangle QTR\): \(\angle QRT=180^\circ-90^\circ-34^\circ=56^\circ\), so \(\angle R=56^\circ\)
In \(\triangle PSR\), \(\angle PSQ\) is the exterior angle at S (Q, S, R lie on one line)
\(\angle PSQ=\angle SPR+\angle PRS=45^\circ+56^\circ=101^\circ\)
So \(x=101\)
