Circles and Central Angles 2 Solving
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Angles ∠BAC and ∠DAE are central angles for circle A. Slider ca1 controls the size of ∠BAC. Slider ca2 controls the size of ∠DAE.
1. If an angle is larger, its arc is __________________.
2. Make ∠DAE and ∠BAC into congruent angles. Drag B and D so the arcs are aligned (on top of one another). If the angles are congruent, how are the arcs related? Try changing the angle lengths to make sure.
3. Can you make both arcs cover the entire circle without overlapping? What is the total of the central angles measures if they do? Is this always the case?
4. Can you make both arcs cover the entire circle without overlapping and have the central angles equal? What kind of angles and arcs do you form?
5. Make EB a diameter and give ∠DAE and ∠BAC two different measurements < 180°. Now solve for the missing angles ∠DAB and ∠CAE. Explain your process.