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Problem of the Week
Problem C
Intersecting Triangles

\(\triangle ABC\) and \(\triangle PQR\) are equilateral triangles with vertices \(B\) and \(P\) on line segment \(MN\). The triangles intersect at two points, \(X\) and \(Y\), as shown.

A horizontal line segment has left endpoint M and right
endpoint N. Triangle ABC has vertex B on MN and side AC above MN, nearly
parallel to MN. Triangle PQR is to the right of triangle ABC with P on
MN and side PR passing through the interior of triangle ABC. PR
intersects AC at X and BC at Y.

If \(\angle NPQ = 75\degree\) and \(\angle MBA = 65\degree\), determine the measure of \(\angle CXY\).

Theme: Geometry & Measurement