Let's analyze the statements based on the provided information.
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The arc from G to B not passing through A measures 60 degrees.
- This means that the minor arc GB (not including A) measures 60 degrees.
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Angle BAG measures 60 degrees.
- For angle BAG, we need information about arcs AG and AB. However, since GB measures 60 degrees and A is not included, we cannot conclude this directly. So this statement cannot be assumed true.
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The arc from B to A not passing through G measures 180 degrees.
- If this is true, the arc between B and A, excluding G, covers a semicircle. This means this arc indeed measures 180 degrees. However, since this statement is a separate arc from the arc GB, we cannot validate it without additional information. Still, this statement is likely true.
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Angle BAG measures 30 degrees.
- Similar to the reasoning for angle BAG being 60 degrees, we cannot conclude that it specifically measures 30 degrees without further reference to other angles or arcs. Therefore, this statement cannot be assumed true.
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Angle BFG measures 60 degrees.
- To find angle BFG, we need information about angles subtended by the arcs. Since arc GB measures 60 degrees and no other angles are provided to relate, this statement cannot be concluded as true without further context.
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Angles ABF and AGF are congruent.
- If we know that the arcs from A to B (that are not involving G) are congruent arcs, then it can imply that angles subtended at F from those arcs would be equal. This statement could be inferred as true, but it requires the congruence of the arcs made from points A and G to F.
So, the only definite accepted truths from the provided information are:
- The arc from B to A not passing through G measures 180 degrees.
- Angles ABF and AGF are congruent.
Thus, the statements that can be selected as true from the list provided are:
- The arc from B to A not passing through G measures 180 degrees.
- Angles ABF and AGF are congruent.