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Answer:
∠BDC = 46°
Explanation:
Angle BDC intercepts arc BC, identified as having a measure of 92°. The angle's vertex, point D, is on the circle, so the angle is called an "inscribed angle." The measure of an inscribed angle is half the measure of the arc it intercepts.
∠BDC = (1/2)arc BC = 1/2(92°)
∠BDC = 46°