In \(\triangle PQR\), S and T are the mid-points of PQ and PR respectively. If \(\angle QPR=95^\circ\) and \(\angle PRQ=35^\circ\), what is the measure of \(\angle TSQ\)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 130°
The line joining the mid-points of two sides of a triangle is parallel to the third side (mid-point theorem). Co-interior angles between parallel lines add up to \(180^\circ\).
\(\angle PQR=180^\circ-95^\circ-35^\circ=50^\circ\)
S and T are mid-points, so \(ST\parallel QR\)
With PQ as the transversal, \(\angle TSQ\) and \(\angle SQR\) are co-interior angles
\(\angle TSQ=180^\circ-50^\circ=130^\circ\)
