# Problem of the Week 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