+20 1. Trapezoid HGFE is inscribed in a circle, with EF || 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.
(btw i will post the next qustions after I see the answer. May the best player win!!)
+9519 arc EH = arc FG
\(x^2 - 2x = 56 - 3x\\ x^2 + x - 56 = 0\\ (x + 8)(x - 7) = 0\\ x = -8\text{(rej.) or }x = 7\\ \)
Both arcs are 35 degrees.
arc EPF = \(360^\circ - 70^\circ - 2\cdot 35^\circ = \boxed{220^\circ}\)
+20 YAY A RIGHT ANSWER
2. In cylic quadrilateral PQRS,
\(\frac{\angle P}{2} = \frac{\angle Q}{3} = \frac{\angle R}{4}.\)
Find the largest angle of quadrilateral PQRS in degrees.
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