11.2.2 Angle Relationships in Circles (continued) Example 5 Finding Arc Measures
The measure of an arc is determined in this example. The measures of two arcs and an angle formed by the two chords and a tangent intersecting the circle are given. The following approach is different, and simpler, than the one illustrated. The measure of SPQ is twice the measure of ∠ USQ according to the Inscribed Angles Theorem, or 160 ° . And = − = PQ m 160 100 60 . Since the measure of the circumference of the circle is 360 ° , = − + + = QT ST SP PQ m 360 (m m m )160.
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