In the diagram, $P T$ and $P S$ are tangents to a circle with centre $O$. The point $Y$ lies on the circumference of the circle; and the point $Z$ is where the line $P Y$ meets the radius $O S$.

Also, $\angle S P Z=10^{\circ}$ and $\angle T O S=150^{\circ}$.

How many degrees are there in the sum of $\angle P T Y$ and $\angle P Y T$ ?
6. 160 The tangent-radius property gives $\angle P S O=\angle P T O=90^{\circ}$. From the angle sum of quadrilateral $P T O S$ we may conclude that $\angle T P S=30^{\circ}$ and therefore that $\angle T P Y=20^{\circ}$. By considering the angle sum of triangle $P T Y$ we conclude that the required total is $160^{\circ}$.