Answer
$\angle TSU+\angle USV=\angle TSV$
$\angle TSV+\angle VSW=\angle TSW$
Therefore, $\angle TSU+\angle USV+\angle VSW=\angle TSW$
Work Step by Step
With angles $\angle TSU$ and $\angle USV$, we can use the Segment Addition Postulate: $\angle TSU+\angle USV=\angle TSV$ (as the drawing shows).
With angles $\angle TSV$ and $\angle VSW$, we can use the Segment Addition Postulate: $\angle TSV+\angle VSW=\angle TSW$ (as the drawing shows).
Using the equations, and substituting $\angle TSV$, we get $\angle TSU+\angle USV+\angle VSW=\angle TSW$.
And now, we proved the Extended Angle Addition Property.
