In the given circle, O is the center, and A, B, C are points on the circle such that B lies on the arc joining A and C (the arc ABC). If the measure of arc ABC (from A to C passing through B) is 130°, what is the value of m∠ABC?
115°
The arc ABC (through B) = 130°, so the remaining arc AC (not containing B) = 360 - 130 = 230°.
The inscribed angle ∠ABC at B subtends the arc AC that does not contain B, so m∠ABC = (1/2) × 230° = 115°. Answer: (B).
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