11.2.2 Angle Relationships in Circles (continued) Example 2 Finding Angle Measures Inside a Circle
If two secants or chords intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs. Another way to think of this is that the measure of the angle is equal to the average of the measures of the arcs it intercepts. The measure of an angle formed by the intersection of two secants inside a circle is determined in this example. The measures of the two intercepted arcs are given. The measure of ∠ BEC equals one-half the sum of AD m and BC m . . Substituting the given values yields m ∠ BEC = 54 ° .
Example 3 Finding Measures Using Tangents and Secants
If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of its intercepted arcs.
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