Trapezoid EFGH is inscribed in a circle, with EF parallel to 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.
+23246 Parallel chords in a circle cut off equal arcs.
Therefore, x2 - 2x = 56 - 3x
---> x2 + x - 56 = 0
(x + 8)(x - 7) = 0
Either x = -8 or x = 7
Since the problem states that x is positive, x = 7
---> x2 - 2x = 72 - 2·7 = 35
56 - 3x = 56 - 3·7 = 35
---> arc(EHGF) = 35o + 70o + 35o = 140o
---> arc(EPF) = 360o - 140o = 220o
