P and Q are two points on a circle with centre at O. R is a point on the minor arc of the circle between the points P and Q. he tangents to the circle at the pints p and Q meet each other at the point S. If $\angle PSQ=\ 20,\ \angle PRQ=?$

The angle between the two tangents is 20 degrees, and since the tangents are perpendicular to the radii, the remaining angle in quadrilateral POSQ is 180 minus 20 degrees which is 160 degrees. This means the central angle POQ equals 160 degrees. The angle subtended by the chord PQ at the minor arc, angle PRQ, is half of the reflex angle POQ. The reflex angle POQ is 360 minus 160 degrees which is 200 degrees, so angle PRQ equals 100 degrees.

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