here is the question
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. here is the pic
I found a list of wrong answers, 205, 210, 240
if someone could please give me the correct answer that would be great
thx in advance
Since GH || EF, arc(EH) = arc(GF) ---> x2 - 2x = 56 - 3x
x2 + x - 56 = 0
(x + 8)(x - 7) = 0
Either x = -8 (not allowed) or x = 7.
arc(EH) = x2 - 2x = (7)2 - 2(7) = 49 - 14 = 35
arc(GF) = 56 - 3x - 56 - 3(7) = 56 - 21 = 35
arc(GH) = 70
arc(EPF) = 360 - arc(EH) - arc(GH) - arc(GF) = 360 - 35 - 70 - 35 = 220