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# Another inscribed angle question, please explain

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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.

Jun 2, 2020

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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).

Jun 2, 2020