Problem C

The Missing Pieces

The following information is known about \(\triangle PQR\).

The point \(S\) is on side \(PR\) and the point \(T\) is on side \(PQ\).

The distance from \(P\) to \(S\) is equal to the distance from \(T\) to \(Q\).

The distance from \(S\) to \(R\) is equal to the distance from \(P\) to \(T\).

\(\angle PRQ=40^{\circ}\) and \(\angle PTS=20^{\circ}\).

Determine the value of each of the five other interior angles. That is, determine the values of \(\angle RPQ\), \(\angle STQ\), \(\angle TQR\), \(\angle RST\), and \(\angle PST\).

**Theme: **Geometry & Measurement