Analyze relationships among inscribed angles, central angles, circumscribed angles, radii, chords, diameters, and tangents.
Find the measure of an exterior angle formed outside a circle from two intercepted arcs
Problem
An exterior angle is formed by \(\text{two}~\text{secants}\). If the intercepted arcs measure \(140^{\circ}\) and \(60^{\circ}\), what is the angle measure?
An exterior secant angle is controlled by separation between two intercepted arcs, not their total. We’ll distinguish the far arc from the near arc, subtract in positive order, and take half of that difference.
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