Based on the analysis of both diagrams, I can now provide a complete solution to the problem.
Solution:
1) Diagram 1:
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Is it an inscribed angle? Yes.
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Name of the angle: ∠BAC (or ∠CAB)
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Intercepted arc: Arc BC
Explanation: In Diagram 1, we have a circle with points A, B, and C on its circumference. The angle is formed at vertex A by chords AB and AC. Since the vertex A lies on the circle and the sides of the angle are chords that intersect the circle at points B and C, this satisfies the definition of an inscribed angle. The intercepted arc is the arc that lies opposite the angle, which is arc BC.
2) Diagram 2:
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Is it an inscribed angle? Yes.
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Name of the angle: ∠LKM (or ∠MKL)
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Intercepted arc: Arc LM
Explanation: In Diagram 2, we have a circle with points L, K, and M on its circumference. The angle is formed at vertex K by chords KL and KM. Since the vertex K lies on the circle and the sides of the angle are chords that intersect the circle at points L and M, this also satisfies the definition of an inscribed angle. The intercepted arc is the arc that lies opposite the angle, which is arc LM.
In summary, both angles shown in the diagrams are inscribed angles. For each, I've identified the angle by its vertex and endpoints, and named the intercepted arc, which is the arc between the two points where the chords intersect the circle (excluding the vertex).
Parent Tip: Review the logic above to help your child master the concept of geometry inscribed angles worksheet answers.
