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UKMT Senior Kangaroo, 2016

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

In the diagram, $PT$ and $PS$ 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 $PY$ meets the radius $OS$ . Also, $\angle SPZ = 10^\circ$ and $\angle TOS = 150^\circ$ . How many degrees are there in the sum of $\angle PTY$ and $\angle PYT$ ?

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