Question

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1 - 3. name the 3 inscribed angles.
4 - 5. name 2 central angles.

Explanation:

Step1: Recall the definition of inscribed angle

An inscribed angle is an angle whose vertex is on the circle and whose sides contain chords of the circle.
For the first circle:

• $\angle BAC$: Vertex \(A\) is on the circle, and sides \(AB\) and \(AC\) are chords.
• $\angle DFC$: Vertex \(F\) is on the circle, and sides \(DF\) and \(CF\) are chords.
• $\angle HGF$: Vertex \(G\) is on the circle, and sides \(HG\) and \(FG\) are chords.

Step2: Recall the definition of central angle

A central angle is an angle whose vertex is at the center of the circle.
For the second circle:

• $\angle IKM$: Vertex \(K\) (center) and sides \(KI\) and \(KM\) (radii).
• $\angle MKL$: Vertex \(K\) (center) and sides \(KM\) and \(KL\) (radii).

Answer:

1 - 3. $\angle BAC$, $\angle DFC$, $\angle HGF$
4 - 5. $\angle IKM$, $\angle MKL$