In \(\triangle PQR\), S and T are the mid-points of PQ and PR respectively. If \(\angle QPR=70^\circ\) and \(\angle PQR=48^\circ\), what is the measure of \(\angle TSQ\)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 132°
By the mid-point theorem, the line joining the mid-points of two sides is parallel to the third side. Then \(\angle TSQ\) and \(\angle SQR\) are co-interior angles, which add up to \(180^\circ\).
S and T are mid-points, so \(ST\parallel QR\)
\(\angle PST=\angle PQR=48^\circ\) (corresponding angles)
P, S, Q lie on one line, so \(\angle TSQ=180^\circ-48^\circ=132^\circ\)
