Trapezoid HGFE is inscribed in a circle, with \(EF \parallel GH\). If arc GH is 70 degrees, arc EH is x^2 - 2x degrees, and arc FG is 56 - 3x degrees, where x > 0, find arc EPF, in degrees.
Parallel lines cut off equal arcs of a circle.
Since EF || GH, arc(EH) = arc(FG).
This means that x2 - 2x = 56 - 3x.
Solve this equation for x.
Use that value of x to find the size of arc(EH) and arc(FG).
The size of arc(GH) is given.
Use these arcs to find the size of arc(EPF).